# Complex Numbers

To begin, please make note of the fact that the name “imaginary number” might give you the impression that these numbers don’t mean anything — that is very far from the truth!  Instead it indicates that there was once a time when people didn’t know what they could measure, so one person in particular (Decartes — remember him?) disparaged them as imaginary.  He was wrong.  They are as meaningful as the real numbers, just in a slightly different context.  They help us to measure many things relating to electricity, and they give us a beautiful and elegant way to change our perspective — to rotate.

A term for the number system we will now begin studying is the “complex numbers.”   For historical reasons, we still call the part of the number that denotes the root of -1 imaginary.

Enjoy!

1. $\rhd$ Introduction to the Imaginary Numbers (5:20) Introduces the number whose square is -1, called $i$, which is *not* wacky, in spite of Sal’s claim
2.  $\rhd$ Simplifying roots of negative numbers (4:04) Simplify numbers like $\sqrt{-52}$.
3. $\star$ Simplifying roots of negative numbers
4. $\rhd$ Powers of the imaginary unit (6:20) Shows how to compute any integer power of $i$, such as $i^{2000}$.
5. $\rhd$ i as the principal root of -1 (6:45) Illustrates the hugely important sequence in which we must simplify radicals including negative numbers and why
6. $\rhd$ Introduction to Complex Numbers (4:43) Adding real and imaginary numbers to get complex numbers