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Q. The real part of $log \,log\, i$ is

COMEDKCOMEDK 2010Complex Numbers and Quadratic Equations

Solution:

$\log\left(\log i\right) = \log \left(\log e^{i\pi/2}\right)$
$ = \log \left(i \frac{\pi}{2}\right) = \log i + \log $
$ = \log \frac{\pi}{2} +\log e^{i\pi /2} = \log \frac{\pi}{2} + \frac{i\pi}{2} $
Hence, real part is $\log \frac{\pi}{2}$.