Question

If $\sin \left(\log i^i\right)=a+ib$.Find $a$ and $b$

Answer 1

$a+ib=\sin \left(\log i^i\right)=\sin \left(i\log i\right)$

$=\sin \left(i(\log \left|i\right|+iampi)\right)$

$=\sin \left(i(0+\frac{i\pi }{2})\right)$

$\therefore a=-1,b=0$