Question

If $z=(i{)}^i$, where $i=\sqrt{-1}$, then Re(z) is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$i=e^{\frac{i\pi }{2}}\Rightarrow z=i^i=(e^{\frac{i\pi }{2}}{)}^i=e^{\frac{-\pi }{2}}$
$\Rightarrow Re\left(z\right)=e^{\frac{-\pi }{2}}$