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 $x$
[Math] Complex exponential with 2 pi
complex numbersexponential function
complex numbersexponential function
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 $x$
Best Answer
That is true if and only if $x\in\mathbb{Z}$, else, I recommend you read on roots of unity.