Complex exponential with 2 pi

Question

I wonder why is it wrong to do the following:

$e^{i2\pi x}=(e^{i2\pi})^x=1^x=1$

for a real $x$ but not for an integer $x$

Answer 1

That is true if and only if $x\in\mathbb{Z}$, else, I recommend you read on roots of unity.