Today in Complex Variables we learned about the de Moivre formula. So, like I do every time I learn a formula named after some dude, I had to look up the dude to see who he was.
Abraham de Moivre lived from 1667 – 1754 (another one of those long-lived mathematicians) and was friends with Newton, Halley, and Stirling, among others.
Originally from France, he moved to London and, while there, became pretty obsessed with Newton’s newly-published Principia Mathematica and basically memorized the material.
In fact, he took Newton’s binomial theorem and was able to generalize it to the multinomial theorem. This work (plus the fact that he was friends with Newton, I’m sure) got him membership in the Royal Society in 1697.
[And—I have to mention it, I’m sorry—he was one of the dudes on Newton’s little crony committee that was put together to hear the plagiarism charges against Leibniz in 1712.]
De Moivre’s famous formula originated (apparently) from this derivation in 1707:
which he later generalized to this form:
Euler proved it using his own Euler’s formula, so that pretty much cinched it. The reason de Moivre’s formula is so important is because it creates quite a nice connection between complex numbers and trigonometry.