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- TL;DR Summary
- I ran into an apparent contradiction when working with Euler's formula and I can't find the mistake.

I differentiated both sides of Euler's formula with respect to

Then for comparison I multiplied both sides of Euler's formula by

Each of these two procedures seems to yield the additive inverse of the other, and I can't seem to figure out why even after a couple of hours of going back over it.

*x*:*e^ix*= sin*x*+*i*cos*x => ie^ix =*cos*x - i*sin*x*

Then for comparison I multiplied both sides of Euler's formula by

*i*:*e^ix*= sin*x*+*i*cos*x => ie^ix = i*sin*x -*cos*x*Each of these two procedures seems to yield the additive inverse of the other, and I can't seem to figure out why even after a couple of hours of going back over it.