Online courses directory (10358)

Design, operation, and management of traffic flows over complex transportation networks are the foci of this course. It covers two major topics: traffic flow modeling and traffic flow operations. Sub-topics include deterministic and probabilistic models, elements of queuing theory, and traffic assignment. Concepts are illustrated through various applications and case studies. This is a half-term subject offered during the second half of the semester.

Through a combination of lectures, cases, and class discussions this subject examines the economic and political conflict between transportation and the environment. It investigates the role of government regulation, green business and transportation policy as facilitators of economic development and environmental sustainability. It analyzes a variety of international policy problems including government-business relations; the role of interest groups, non-governmental organizations, and the public and media in the regulation of the automobile; sustainable development; global warming; the politics of risk and siting of transport facilities; environmental justice; equity; and transportation and public health in the urban metropolis. It provides students with an opportunity to apply transportation and planning methods to developing policy alternatives in the context of environmental politics.

This class surveys the current concepts, theories, and issues in strategic management of transportation organizations. It provides transportation logistics and engineering systems students with an overview of the operating context, leadership challenges, strategies, and management tools that are used in today's public and private transportation organizations. The following concepts, tools, and issues are presented in both public and private sector cases: alternative models of decision-making, strategic planning (e.g., use of SWOT analysis and scenario development), stakeholder valuation and analysis, government-based regulation and cooperation within the transportation enterprise, disaster communications, systems safety, change management, and the impact of globalization.

Approaching transportation as a complex, large-scale, integrated, open system (CLIOS), this course strives to be an interdisciplinary systems subject in the "open" sense. It introduces qualitative modeling ideas and various techniques and philosophies of modeling complex transportation enterprises. It also introduces conceptual frameworks for qualitative analysis, such as frameworks for regional strategic planning, institutional change analysis, and new technology development and deployment. And it covers transportation as a large-scale, integrated system that interacts directly with the social, political, and economic aspects of contemporary society. Fundamental elements and issues shaping traveler and freight transportation systems are covered, along with underlying principles governing transportation planning, investment, operations, and maintenance.

The main objective of this course is to give broad insight into the different facets of transportation systems, while providing a solid introduction to transportation demand and cost analyses. As part of the core in the Master of Science in Transportation program, the course will not focus on a specific transportation mode but will use the various modes to apply the theoretical and analytical concepts presented in the lectures and readings.

Introduces transportation systems analysis, stressing demand and economic aspects. Covers the key principles governing transportation planning, investment, operations and maintenance. Introduces the microeconomic concepts central to transportation systems. Topics covered include economic theories of the firm, the consumer, and the market, demand models, discrete choice analysis, cost models and production functions, and pricing theory. Application to transportation systems include congestion pricing, technological change, resource allocation, market structure and regulation, revenue forecasting, public and private transportation finance, and project evaluation; covering urban passenger transportation, freight, aviation and intelligent transportation systems.

Este curso se imparte en español con subtítulos en inglés, y tanto el material adicional como los ejercicios del curso se ofrecerán en español e inglés. / This course will be taught in Spanish with English subtitles; the required readings as well as the quizzes and other evaluation materials will be provided in both languages.

Desde que en 1954 se realizara el primer trasplante exitoso de un órgano, la cirugía de trasplantes se ha desarrollado espectacularmente brindando esperanza y calidad de vida a muchos enfermos. Mientras esas técnicas y posibilidades terapéuticas avanzan, persisten sin embargo muchos interrogantes sobre el modo en el que los órganos pueden obtenerse lícitamente. Algunos de esos dilemas nos acompañan desde siempre, otros son suscitados por la aparición de fenómenos novedosos como el turismo de trasplantes, las posibilidades que ofrece la donación tras la muerte cardiocirculatoria o los descubrimientos sobre las funciones fisiológicas remanentes en los pacientes diagnosticados en muerte cerebral. En la inmensa mayoría de los países no se pueden comprar y vender órganos. ¿Por qué? A pesar de que muchas personas siguen muriendo a la espera de recibir un órgano, en ningún país se confiscan los órganos de las personas fallecidas. ¿Por qué? ¿Pueden donar los menores? ¿Debemos prescindir de la conocida como “regla del donante cadáver” y permitir la eutanasia para la donación? ¿Con qué límites? ¿De qué manera influye la potencial condición de donante de un órgano en los cuidados que se proporcionan al final de la vida? ¿Cómo evitar el conflicto de intereses entre quienes velan por la vida de los futuros receptores de un órgano y quienes aún se afanan por cuidar a quien va a fallecer de manera irremisible e inminente?

En este curso nos adentraremos en el análisis de ésas y otras cuestiones, pero también introduciremos los nuevos desafíos que para la ética y el Derecho plantean trasplantes novedosos así como la discusión en torno a los criterios de justa distribución de los órganos
 
The first successful organ transplantation was performed in 1954. Since then, the technique has evolved tremendously, giving hope and increased quality of life to many patients around the world. While the technology and drugs advance, several controversies persist regarding the way in which organs may be obtained. Some of these dilemmas arose on the very first day in which organs’ transplantation originated; others have emerged as a result of new phenomena such as transplantation tourism, the new possibilities brought by donation after cardio-circulatory death, or increasing knowledge about the remaining physiological functions detected in patients pronounced as brain dead. Almost all countries in the world forbid the selling of organs. Why? Although many people die while on the waiting lists, in no country does the Government confiscate cadaveric organs. Why? May minors be organ donors? Should we abandon the so-called “dead donor rule” and allow “organ-donation euthanasia”? How does the potential condition of becoming a donor influence the administration of end-of-life care? How should we avoid the eventual conflict of interests between those who care for the life of future recipients of organs and those who are in charge of the dying patient-eventual-donor? In this course we will explore the answers to these questions, and we will also engage in the assessment of the more recent challenges posed by novel transplantation techniques, and, albeit briefly, in the discussion regarding the fair distribution of organs. 

In the western world, approximately 10–15% of couples suffer from subfertility. Consequently, over 5 million babies have been born thanks to assisted reproductive technologies, and more than half of those have been born in the past six years alone. This class will cover the basic biology behind fertility and explore the etiology of infertility. We will highlight open questions in reproductive biology, familiarize students with both tried-and-true and emerging reproductive technologies, and explore the advantages and pitfalls of each.

This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. Many instructors of the Advanced Undergraduate Seminars are postdoctoral scientists with a strong interest in teaching.

This course explores a variety of electronic applications used in the promotion of healthy behavior, focusing on cases relating to physical health (electronic cigarettes), mental health (apps and wearables), and social health (e-mediation). In each of these areas, experts will share cutting-edge scientific knowledge and demonstrate some of the latest e-applications to boost healthy behavior. The course consists of 3 modules:

1. e-Cigarette: Promoting physical health. In this module, you will learn about the potential implications of e-cigarettes as a Tobacco Harm Reduction Strategy. You will gain contemporary scientific knowledge about the safety, efficacy, and potential health threats of using e-cigarettes.
2. e-Mental Health: Promoting mental health. In this module, you will learn about innovations in online, mobile and wearable tools used in mental healthcare (a rapidly expanding field), as well as their potential advantages and disadvantages.
3. e-Mediation: Promoting social health. In this module, you will learn about the core principles of mediation, and how you can use electronic communication to prevent escalation and promote conflict resolution during the mediation process.

This MOOC consists of knowledge clips, demonstration movies, exercises, discussion, and homework (reading) assignments.

This seminar examines a number of famous trials in European and American history. It considers the salient issues (political, social, cultural) of several trials, the ways in which each trial was constructed and covered in public discussions at the time, the ways in which legal reasoning and storytelling interacted in each trial and in the later retellings of the trial, and the ways in which trials serve as both spectacle and a forum for moral and political reasoning. Students have an opportunity to study one trial in depth and present their findings to the class.

This course addresses the design of tribological systems: the interfaces between two or more bodies in relative motion. Fundamental topics include: geometric, chemical, and physical characterization of surfaces; friction and wear mechanisms for metals, polymers, and ceramics, including abrasive wear, delamination theory, tool wear, erosive wear, wear of polymers and composites; and boundary lubrication and solid-film lubrication. The course also considers the relationship between nano-tribology and macro-tribology, rolling contacts, tribological problems in magnetic recording and electrical contacts, and monitoring and diagnosis of friction and wear. Case studies are used to illustrate key points.

Curso de Trigonometr

The foundations of Trigonometry from The Khan Academy.

Videos on trigonometry. Watch the "Geometry" playlist first if you have trouble understanding the topics covered here. Basic Trigonometry. Basic Trigonometry II. Radians and degrees. Using Trig Functions. Using Trig Functions Part II. The unit circle definition of trigonometric function. Unit Circle Definition of Trig Functions. Graph of the sine function. Graphs of trig functions. Graphing trig functions. More trig graphs. Determining the equation of a trigonometric function. Trigonometric Identities. Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b). Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b). Trig identities part 2 (parr 4 if you watch the proofs). Trig identies part 3 (part 5 if you watch the proofs). Trigonometry word problems (part 1). Trigonometry word problems (part 2). Law of cosines. Navigation Word Problem. Proof: Law of Sines. Ferris Wheel Trig Problem. Ferris Wheel Trig Problem (part 2). Fun Trig Problem. Polar Coordinates 1. Polar Coordinates 2. Polar Coordinates 3. Inverse Trig Functions: Arcsin. Inverse Trig Functions: Arctan. Inverse Trig Functions: Arccos. Trigonometry Identity Review/Fun. Tau versus Pi. IIT JEE Trigonometry Problem 1. IIT JEE Trigonometric Maximum. IIT JEE Trigonometric Constraints. Trigonometric System Example. 2003 AIME II Problem 11.avi. 2003 AIME II Problem 14.

Basic trigonometry. Example: Using soh cah toa. Trigonometry 0.5. Basic trigonometry II. Trigonometry 1. Secant (sec), cosecant (csc) and cotangent (cot) example. Example: Using trig to solve for missing information. Reciprocal trig functions. Trigonometry 1.5. Example: Calculator to evaluate a trig function. Example: Trig to solve the sides and angles of a right triangle. Trigonometry 2. Example: Solving a 30-60-90 triangle. Special right triangles. Using Trig Functions. Using Trig Functions Part II. Introduction to radians. Radian and degree conversion practice. Example: Radian measure and arc length. Example: Converting degrees to radians. Degrees to radians. Example: Converting radians to degrees. Radians to degrees. Radians and degrees. Radians and degrees. Unit circle definition of trig functions. Example: Unit circle definition of sin and cos. Example: Using the unit circle definition of trig functions. Example: Trig function values using unit circle definition. Example: The signs of sine and cosecant. Unit Circle Manipulative. Unit circle. Example: Graph, domain, and range of sine function. Example: Graph of cosine. Example: Intersection of sine and cosine. Example: Amplitude and period. Example: Amplitude and period transformations. Example: Amplitude and period cosine transformations. Example: Figure out the trig function. Graphs of sine and cosine. Graph of the sine function. Graphs of trig functions. Graphing trig functions. More trig graphs. Determining the equation of a trigonometric function. Inverse Trig Functions: Arcsin. Inverse Trig Functions: Arccos. Inverse Trig Functions: Arctan. Example: Calculator to evaluate inverse trig function. Inverse trig functions. Tau versus Pi. Pi Is (still) Wrong.. Basic trigonometry. Example: Using soh cah toa. Trigonometry 0.5. Basic trigonometry II. Trigonometry 1. Secant (sec), cosecant (csc) and cotangent (cot) example. Example: Using trig to solve for missing information. Reciprocal trig functions. Trigonometry 1.5. Example: Calculator to evaluate a trig function. Example: Trig to solve the sides and angles of a right triangle. Trigonometry 2. Example: Solving a 30-60-90 triangle. Special right triangles. Using Trig Functions. Using Trig Functions Part II. Introduction to radians. Radian and degree conversion practice. Example: Radian measure and arc length. Example: Converting degrees to radians. Degrees to radians. Example: Converting radians to degrees. Radians to degrees. Radians and degrees. Radians and degrees. Unit circle definition of trig functions. Example: Unit circle definition of sin and cos. Example: Using the unit circle definition of trig functions. Example: Trig function values using unit circle definition. Example: The signs of sine and cosecant. Unit Circle Manipulative. Unit circle. Example: Graph, domain, and range of sine function. Example: Graph of cosine. Example: Intersection of sine and cosine. Example: Amplitude and period. Example: Amplitude and period transformations. Example: Amplitude and period cosine transformations. Example: Figure out the trig function. Graphs of sine and cosine. Graph of the sine function. Graphs of trig functions. Graphing trig functions. More trig graphs. Determining the equation of a trigonometric function. Inverse Trig Functions: Arcsin. Inverse Trig Functions: Arccos. Inverse Trig Functions: Arctan. Example: Calculator to evaluate inverse trig function. Inverse trig functions. Tau versus Pi. Pi Is (still) Wrong..

A detailed look at shapes that are prevalent in science: conic sections. Introduction to Conic Sections. Recognizing conic sections. Radius and center for a circle equation in standard form. Equation of a circle in factored form. Conic Sections: Intro to Circles. Graphing circles. Equation of a circle in non-factored form. Graphing circles 2. Conic Sections: Intro to Ellipses. Equation of an ellipse. Foci of an Ellipse. Parabola Focus and Directrix 1. Focus and Directrix of a Parabola 2. Parabola intuition 1. Parabola intuition 2. Conic Sections: Intro to Hyperbolas. Conic Sections: Hyperbolas 2. Conic Sections: Hyperbolas 3. Equation of a hyperbola. Foci of a Hyperbola. Proof: Hyperbola Foci. Identifying an ellipse from equation. Identifying a hyperbola from an equation. Identifying circles and parabolas from equations. Hyperbola and parabola examples. Tangent Line Hyperbola Relationship (very optional). IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Circle Hyperbola Intersection. Introduction to Conic Sections. Recognizing conic sections. Radius and center for a circle equation in standard form. Equation of a circle in factored form. Conic Sections: Intro to Circles. Graphing circles. Equation of a circle in non-factored form. Graphing circles 2. Conic Sections: Intro to Ellipses. Equation of an ellipse. Foci of an Ellipse. Parabola Focus and Directrix 1. Focus and Directrix of a Parabola 2. Parabola intuition 1. Parabola intuition 2. Conic Sections: Intro to Hyperbolas. Conic Sections: Hyperbolas 2. Conic Sections: Hyperbolas 3. Equation of a hyperbola. Foci of a Hyperbola. Proof: Hyperbola Foci. Identifying an ellipse from equation. Identifying a hyperbola from an equation. Identifying circles and parabolas from equations. Hyperbola and parabola examples. Tangent Line Hyperbola Relationship (very optional). IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Circle Hyperbola Intersection.

An look at exponential and logarithmic functions including many of their properties and graphs. Exponential Growth Functions. Ex: Graphing exponential functions. Subtracting Rational Expressions. Word Problem Solving- Exponential Growth and Decay. Exponential Growth. Graphing Logarithmic Functions. Logarithmic Scale. Vi and Sal Explore How We Think About Scale. Vi and Sal Talk About the Mysteries of Benford's Law. Benford's Law Explanation (Sequel to Mysteries of Benford's Law). Solving Logarithmic Equations. Solving Logarithmic Equations. Introduction to interest. Interest (part 2). Introduction to compound interest and e. Compound Interest and e (part 2). Compound Interest and e (part 3). Compound Interest and e (part 4). Exponential Growth Functions. Ex: Graphing exponential functions. Subtracting Rational Expressions. Word Problem Solving- Exponential Growth and Decay. Exponential Growth. Graphing Logarithmic Functions. Logarithmic Scale. Vi and Sal Explore How We Think About Scale. Vi and Sal Talk About the Mysteries of Benford's Law. Benford's Law Explanation (Sequel to Mysteries of Benford's Law). Solving Logarithmic Equations. Solving Logarithmic Equations. Introduction to interest. Interest (part 2). Introduction to compound interest and e. Compound Interest and e (part 2). Compound Interest and e (part 3). Compound Interest and e (part 4).

Revisiting what a function is and how we can define and visualize one. What is a function. Function example problems. Ex: Constructing a function. Functions Part 2. Functions as Graphs. Understanding function notation exercise. Understanding function notation. Functions (Part III). Functions (part 4). Sum of Functions. Difference of Functions. Product of Functions. Quotient of Functions. Evaluating expressions with function notation. Evaluating composite functions. Domain of a function. Domain of a function. Domain of a function. Domain and Range of a Relation. Domain and range from graph. Domain and Range of a Function Given a Formula. Domain and Range 1. Domain of a Radical Function. Domain of a function. Domain and Range 2. Domain and Range of a Function. Range of a function. Introduction to Function Inverses. Function Inverse Example 1. Function Inverses Example 2. Function Inverses Example 3. Inverses of functions. When a function is positive or negative. Positive and negative parts of functions. Recognizing odd and even functions. Connection between even and odd numbers and functions. Even and odd functions. Shifting and reflecting functions. Shifting functions. Shifting and reflecting functions. Recognizing features of functions (Example 1). Recognizing features of functions 2 (example 2). Recognizing features of functions 2 (example 3). Recognizing features of functions 2. Interpreting features of functions 2 (Example 1). Interpreting features of functions 2 (Example 2). Interpreting features of functions 2. Comparing features of functions 2 (example 1). Comparing features of functions 2 (example 2). Comparing features of functions 2 (example 3). Comparing features of functions 2. Why Dividing by Zero is Undefined. Why Zero Divided by Zero is Undefined/Indeterminate. Undefined and Indeterminate. A more formal understanding of functions. Introduction to the inverse of a function. What is a function. Function example problems. Ex: Constructing a function. Functions Part 2. Functions as Graphs. Understanding function notation exercise. Understanding function notation. Functions (Part III). Functions (part 4). Sum of Functions. Difference of Functions. Product of Functions. Quotient of Functions. Evaluating expressions with function notation. Evaluating composite functions. Domain of a function. Domain of a function. Domain of a function. Domain and Range of a Relation. Domain and range from graph. Domain and Range of a Function Given a Formula. Domain and Range 1. Domain of a Radical Function. Domain of a function. Domain and Range 2. Domain and Range of a Function. Range of a function. Introduction to Function Inverses. Function Inverse Example 1. Function Inverses Example 2. Function Inverses Example 3. Inverses of functions. When a function is positive or negative. Positive and negative parts of functions. Recognizing odd and even functions. Connection between even and odd numbers and functions. Even and odd functions. Shifting and reflecting functions. Shifting functions. Shifting and reflecting functions. Recognizing features of functions (Example 1). Recognizing features of functions 2 (example 2). Recognizing features of functions 2 (example 3). Recognizing features of functions 2. Interpreting features of functions 2 (Example 1). Interpreting features of functions 2 (Example 2). Interpreting features of functions 2. Comparing features of functions 2 (example 1). Comparing features of functions 2 (example 2). Comparing features of functions 2 (example 3). Comparing features of functions 2. Why Dividing by Zero is Undefined. Why Zero Divided by Zero is Undefined/Indeterminate. Undefined and Indeterminate. A more formal understanding of functions. Introduction to the inverse of a function.

Thinking about graphing on a coordinate plane, slope and other analytic geometry. Descartes and Cartesian Coordinates. The Coordinate Plane. Plot ordered pairs. Graphing points. Quadrants of Coordinate Plane. Graphing points and naming quadrants. Points on the coordinate plane. Ordered pair solutions of equations. Ordered Pair Solutions of Equations 2. Ordered pair solutions to linear equations. Recognizing Linear Functions. Interpreting linear relationships. Slope of a line. Slope of a Line 2. Slope and Rate of Change. Graphical Slope of a Line. Slope of a Line 3. Identifying slope of a line. Slope and Y-intercept Intuition. Line graph intuition. Graphing a line in slope intercept form. Converting to slope-intercept form. Graphing linear equations. Multiple examples of constructing linear equations in slope-intercept form. Constructing equations in slope-intercept form from graphs. Constructing linear equations to solve word problems. Linear equation from slope and a point. Finding a linear equation given a point and slope. Constructing the equation of a line given two points. Solving for the y-intercept. Slope intercept form. Linear Equations in Point Slope Form. Point slope form. Linear Equations in Standard Form. Point-slope and standard form. Converting between slope-intercept and standard form. Converting between point-slope and slope-intercept. Finding the equation of a line. Midpoint formula. Midpoint formula. Distance Formula. Distance formula. Perpendicular Line Slope. Equations of Parallel and Perpendicular Lines. Parallel Line Equation. Parallel Lines. Parallel Lines 2. Parallel lines 3. Perpendicular Lines. Perpendicular lines 2. Equations of parallel and perpendicular lines. Distance between point and line. Graphing Inequalities. Solving and graphing linear inequalities in two variables 1. Graphing Linear Inequalities in Two Variables Example 2. Graphing Inequalities 2. Graphing linear inequalities in two variables 3. Graphs of inequalities. Graphing linear inequalities. Graphing and solving linear inequalities. Descartes and Cartesian Coordinates. The Coordinate Plane. Plot ordered pairs. Graphing points. Quadrants of Coordinate Plane. Graphing points and naming quadrants. Points on the coordinate plane. Ordered pair solutions of equations. Ordered Pair Solutions of Equations 2. Ordered pair solutions to linear equations. Recognizing Linear Functions. Interpreting linear relationships. Slope of a line. Slope of a Line 2. Slope and Rate of Change. Graphical Slope of a Line. Slope of a Line 3. Identifying slope of a line. Slope and Y-intercept Intuition. Line graph intuition. Graphing a line in slope intercept form. Converting to slope-intercept form. Graphing linear equations. Multiple examples of constructing linear equations in slope-intercept form. Constructing equations in slope-intercept form from graphs. Constructing linear equations to solve word problems. Linear equation from slope and a point. Finding a linear equation given a point and slope. Constructing the equation of a line given two points. Solving for the y-intercept. Slope intercept form. Linear Equations in Point Slope Form. Point slope form. Linear Equations in Standard Form. Point-slope and standard form. Converting between slope-intercept and standard form. Converting between point-slope and slope-intercept. Finding the equation of a line. Midpoint formula. Midpoint formula. Distance Formula. Distance formula. Perpendicular Line Slope. Equations of Parallel and Perpendicular Lines. Parallel Line Equation. Parallel Lines. Parallel Lines 2. Parallel lines 3. Perpendicular Lines. Perpendicular lines 2. Equations of parallel and perpendicular lines. Distance between point and line. Graphing Inequalities. Solving and graphing linear inequalities in two variables 1. Graphing Linear Inequalities in Two Variables Example 2. Graphing Inequalities 2. Graphing linear inequalities in two variables 3. Graphs of inequalities. Graphing linear inequalities. Graphing and solving linear inequalities.

Motivation and understanding of hyperbolic trig functions. Hyperbolic Trig Function Inspiration. Hyperbolic Trig Functions and the Unit Hyperbola. Hyperbolic Trig Function Inspiration. Hyperbolic Trig Functions and the Unit Hyperbola.

Understanding i and the complex plane. Introduction to i and Imaginary Numbers. Calculating i Raised to Arbitrary Exponents. Imaginary unit powers. Imaginary Roots of Negative Numbers. i as the Principal Root of -1 (a little technical). Complex numbers. Complex numbers (part 1). Complex numbers (part 2). The complex plane. Adding Complex Numbers. Subtracting Complex Numbers. Complex number polar form intuition. Complex plane operations. Adding and subtracting complex numbers. Multiplying Complex Numbers. Multiplying complex numbers. Dividing Complex Numbers. Dividing complex numbers. Multiplying and dividing complex numbers in polar form. Complex Conjugates. Complex Conjugates Example. Absolute value of complex numbers. Basic Complex Analysis. Complex number polar form intuition exercise. Complex number polar form intuition. Exponential form to find complex roots. Multiplying and dividing complex numbers in polar form. Powers of complex numbers. Complex Conjugates. IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). Complex Determinant Example. Introduction to i and Imaginary Numbers. Calculating i Raised to Arbitrary Exponents. Imaginary unit powers. Imaginary Roots of Negative Numbers. i as the Principal Root of -1 (a little technical). Complex numbers. Complex numbers (part 1). Complex numbers (part 2). The complex plane. Adding Complex Numbers. Subtracting Complex Numbers. Complex number polar form intuition. Complex plane operations. Adding and subtracting complex numbers. Multiplying Complex Numbers. Multiplying complex numbers. Dividing Complex Numbers. Dividing complex numbers. Multiplying and dividing complex numbers in polar form. Complex Conjugates. Complex Conjugates Example. Absolute value of complex numbers. Basic Complex Analysis. Complex number polar form intuition exercise. Complex number polar form intuition. Exponential form to find complex roots. Multiplying and dividing complex numbers in polar form. Powers of complex numbers. Complex Conjugates. IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). Complex Determinant Example.