lllllllllllllllllllllllllll Theorem

After looking over the teaching standards, I came across one standard that was unknown to my educational experience; "State, prove, and use De Moivre's Theorem." After a moment's pause, I took a few deep breathes and ventured to the mysterious realm of Google in search of De Moivre's Theorem. Following the click of the search button, I came across a theorem more fierce than I had ever experienced. It was the De Moivre's Theorem. For those of you still reading along and need to...


If the complex number z= r(cos a + sin a), then

Which as I scroll down the page I find that:

If  z = r (cos a + sin a), and n is a natural number, then

Horrified by the events that had unfolded, I felt faint, sick, and a little hungry. I became very dizzy, and my head and computer desk came together with a thud. 

Thank you, Cliff Notes, for the theorem and pictures. For information on the theorem: Yay!