Question

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

• A. $\frac{\pi}{2}$
• B. $\log \frac{\pi}{2}$
• C. $0$
• D. $none\, of\, these$

Answer 1

Answer: (B)

$\log \frac{\pi}{2}$

Answer 2

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