Euler’s formula (well, one of Euler’s formulas) states that The proof I am most familiar with is based on the Maclaurin series for , and .

I ran across a different, simpler proof recently on Math Stack Exchange, posted by user02138. It doesn’t give any insight into why the formula is true, but it is very short.

Let . Then Simplifying, we have The fact that implies that for some constant *C*. Since and thus

Some of the other answers to “How to prove Euler’s formula” are interesting and worth perusing as well.

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