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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.

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  • $\begingroup$ How do you know the answer? Note that $e^{i \pi/2} = i$ rather than $i \pi/2$ $\endgroup$ – Henry Jun 23 '14 at 17:40
  • $\begingroup$ Are you asking about $\log(i)$ or $\log( \pi i / 2)$? $\endgroup$ – Omnomnomnom Jun 23 '14 at 17:47
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Hint

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

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

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  • $\begingroup$ What does $\mathbb{C^*}$ denote (as opposed just to $\mathbb{C}$)? $\endgroup$ – beep-boop Jun 23 '14 at 18:25
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    $\begingroup$ $\mathbb{C}^* = \mathbb{C}\setminus\{0\}$ $\endgroup$ – user41489 Jun 23 '14 at 18:35
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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, $log(i\pi/2)=log(\pi/2)+i(\pi/2+2n\pi)$, $n\in\mathbb{Z}$.

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