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}^+](http://s0.wp.com/latex.php?latex=z%5En%3D%28a%2Bbi%29%5En%3Dr%5En+%5Ccdot+%5Cleft%5B+%5Ccos%5Cleft%28n%5Ctheta%5Cright%29%2Bi%5Csin%28n%5Ctheta%29%5Cright%5D%5Cmid+n%5Cin+%5Cmathbb%7BZ%7D%5E%2B&bg=ffffff&fg=000000&s=0 "z^n=(a+bi)^n=r^n \cdot \left[ \cos\left(n\theta\right)+i\sin(n\theta)\right]\mid n\in \mathbb{Z}^+")
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