Question

The real part of $loglogi$ is

• A. $\frac{\pi }{2}$
• B. $\log \frac{\pi }{2}$
• C. $0$
• D. $noneofthese$

Answer 1

Answer: (B)

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