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?

Consider the following:
Let $z=a+bi$ where $a,b$ belong to the set of all real number.
We would like to solve for $a$ and $b$ such that $z^2=i$, that is $(a+bi)^2=0+i$
Then, you will know why $\sqrt{i}= \frac{1+i}{\sqrt{2}}$ and how to solve your problem.
