# Complex numbers

This topic covers: - Adding, subtracting, multiplying, & dividing complex numbers - Complex plane - Absolute value & angle of complex numbers - Polar coordinates of complex numbers

This course contains 11 segments:

**What are the imaginary numbers?**

Learn about the imaginary unit i (which is the square root of -1) and about imaginary numbers like 3i (which is the square root of -9).

**What are the complex numbers?**

Learn about complex numbers (spoiler: they are numbers that consist of both real and imaginary parts).

**The complex plane**

Learn how we can visualize complex numbers in a plane. This can be seen as an expansion of the 1-dimensional real number line into a 2-dimensional plane!

**Adding & subtracting complex numbers**

Learn how to add or subtract complex numbers. For example, write (2+3i)-(1+2i) as (1+i).

**Multiplying complex numbers**

Learn how to multiply complex numbers using the fact that i^2=-1 and the distributive property. For example, multiply (1+i) by (2+3i).

**Complex conjugates & dividing complex numbers**

Learn how to divide complex numbers using the conjugate of the divisor. For example, divide (2+3i) by (-1+4i) by multiplying both the dividend and the divisor by (-1-4i).

**Absolute value & angle of complex numbers**

Learn about very important graphical features of complex numbers: their absolute value and their angle.

**Distance & midpoint of complex numbers**

Learn how we define the distance of two complex numbers, and how we define their midpoint.

**Polar form of complex numbers**

Learn how to represent complex numbers in a different way. Unlike rectangular form, which emphasizes the real and imaginary parts, polar form emphasizes the absolute value ("modulus") and the angle ("argument").

**Multiplying & dividing complex numbers in polar form**

Learn how complex multiplication and division work when the numbers are given in polar form. Amazingly enough, this is much easier than multiplication and division in rectangular form.

**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.

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Length | 11 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math Algebra |

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Rating | Not enough ratings |
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Length | 11 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math Algebra |

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