Can anyone tell me how $\frac{\pi}{\sqrt 2} = \frac{\pi + i\pi}{2\sqrt i}$ I was working out a problem last night and got the result
$\frac{\pi + i\pi}{2\sqrt i}$
However, WolframAlpha gave the result
$\frac{\pi}{\sqrt 2}$
Upon closer inspection I found out that
$\frac{\pi}{\sqrt 2} = \frac{\pi + i\pi}{2\sqrt i}$
But I cant seem to derive it myself and it has been bugging me all day. How can this complex number be reduced to a real number?

Rewriting everything in polar form, the numerator is $\sqrt{2} \pi e^{i \pi/4}$ and the denominator is, for the choice of branch of $\sqrt{}$ that Wolfram is using, $2 e^{i \pi/4}$. So the $e^{i \pi/4}$ terms cancel and you're left with a real number.
