## An Imaginary Tale: De Moivre’s Formula in a Gif

I’ve been reading the book, An Imaginary Tale: The Story of i [the square root of minus one] by Paul J. Nahin and it’s really interesting!  I’m almost to chapter 4 and so far it’s been introducing some nifty ideas about complex numbers.  Among the content, we find a very convenient way of calculating the value of a complex number when multiplied by itself an integer amount of times.  That is, $z^n=(a+bi)^n=r^n \cdot \left[ \cos\left(n\theta\right)+i\sin(n\theta)\right]\mid n\in \mathbb{Z}^+$.  This is De Moivre’s Formula.

## Did You Know: i^i Is Real?

In my last post, A REALLY Brief Intro to Complex Numbers, I talked about a few necessary definitions to know what Complex numbers $\mathbb{C}$ are.  Complex numbers are really intriguing and necessary for our electronic devices to work.  You might be reading this on a computer, smartphone, tablet, etc., but none of the advances in technology would be possible without use of complex numbers.  Creating wonders from wonders.

## A REALLY Brief Intro to Complex Numbers

Venn Diagram of Number Sets from Keith’s Think Zone

Imaginary numbers and complex numbers interest me a lot.  Aside from the properties of infinity ($\infty$), complex numbers $\mathbb{C}$ are, well… complex! They’re very strange and yet they open a whole new world of numbers beyond the Real numbers $\mathbb{R}$.