Question

The imaginary part of $i^i$ is

• A. 1
• B. 0
• C. -1
• D. 2

Answer 1

Answer: (B)

Let $(a+ib)=i^i$
Taking log on both sides, we get
$\log \left(a+ib\right)=i\log i$
$\Rightarrow \log \left(a+ib\right)=i\left(i\pi /2\right)$
$\Rightarrow \log \left(a+ib\right)=-\frac{\pi }{2}$
$\Rightarrow \left(a+ib\right)=e^{-\pi /2}$
On comparing imaginary part of $i^i$ is 0.