Help me to solve math homework on logarithmic

Question

How to solve this math home work? Please help..

What is the value of $\log \left(\dfrac{i\pi}{2}\right)$ ?

I got to know the answer is "$\dfrac{i\pi}{2}$", but don't know how to solve it. Please help me.

Thanks a lot in advance.

Answer 1

Hint

For $z\in\Bbb C^*$ we have

$$\ln z=\ln|z|+i\arg z$$

Answer 2

Using this

$log z=log|z|+iarg(z)$

you should be able to get $|i\pi/2|=\pi/2$ and $arg(i\pi/2)=\pi/2$ thus, $log(i\pi/2)=log(\pi/2)+i(\pi/2+2n\pi)$, $n\in\mathbb{Z}$.