Is it true that $e^{\frac{i}{2}\pi}+e^{-\frac{i}{2}\pi}=0$? As in the title. Is it true that:
$$e^{\frac{i}{2}\pi}+e^{-\frac{i}{2}\pi}=0$$
And if it indeed is, how could one prove it? Maybe it's a silly question, but - frankly I'm kinda new to complex exponentials. 

By Euler's formula,
$$ e^{\frac{i\pi}{2}}=\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}=i $$
and 
$$ e^{\frac{-i\pi}{2}}=\cos\Big(-\frac{\pi}{2}\Big)+i\sin\Big(-\frac{\pi}{2}\Big)=-i $$
hence the sum is zero.
