Khan Academy on a Stick : Imaginary and complex numbers

Khan Academy on a Stick

Trigonometry and precalculus

Introduction to i and Imaginary Numbers
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Introduction to i and imaginary numbers
Calculating i Raised to Arbitrary Exponents
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Calculating i raised to arbitrarily high exponents
Imaginary Roots of Negative Numbers
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Imaginary Roots of Negative Numbers
i as the Principal Root of -1 (a little technical)
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i as the principal square root of -1

The imaginary unit i

This is where math starts to get really cool. It may see strange to define a number whose square is negative one. Why do we do this? Because it fits a nice niche in the math ecosystem and can be used to solve problems in engineering and science (not to mention some of the coolest fractals are based on imaginary and complex numbers). The more you think about it, you might realize that all numbers, not just i, are very abstract.

Complex numbers
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Complex Numbers
Complex numbers (part 1)
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Introduction to complex numbers. Adding, subtracting and multiplying complex numbers.
Complex numbers (part 2)
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Dividing complex numbers. Complex conjugates.
Adding Complex Numbers
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Adding Complex Numbers
Subtracting Complex Numbers
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Subtracting Complex Numbers
Multiplying Complex Numbers
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Multiplying Complex Numbers
Dividing Complex Numbers
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Dividing Complex Numbers
Complex Conjugates
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Complex Conjugates
Complex Conjugates Example
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Complex Conjugates

Complex numbers

Let's start constructing numbers that have both a real and imaginary part. We'll call them complex. We can even plot them on the complex plane and use them to find the roots of ANY quadratic equation. The fun must not stop!

Basic Complex Analysis
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Argand Diagram, magnitude, modulus, argument, exponential form
Exponential form to find complex roots
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Using exponential form to find complex roots
Complex Conjugates
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Complex Conjugates

Intro to complex analysis

You know what imaginary and complex numbers are, but want to start digging a bit deeper. In this tutorial, we will explore different ways of representing a complex number and finding its roots.

IIT JEE Complex Numbers (part 1)
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2010 IIT JEE Paper 1 Problem 39 Complex Numbers (part 1)
IIT JEE Complex Numbers (part 2)
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2010 IIT JEE Paper 1 Problem 39 Complex Numbers (part 2)
IIT JEE Complex Numbers (part 3)
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2010 IIT JEE Paper 1 Problem 39 Complex Numbers (part 3)
Complex Determinant Example
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2010 IIT JEE Paper 1 Problem 53 Complex Determinant

Challenging complex number problems

This tutorial goes through a fancy problem from the IIT JEE exam in India (competitive exam for getting into their top engineering schools). Whether or not you live in India, this is a good example to test whether you are a complex number rock star.