Question

If $z=(i{)}^{(i{)}^{\left(i\right)}}$ where $i=\sqrt{-1}$, then $z$ is equal to

• A. $-i$
• B. $-1$
• C. $1$
• D. $i$

Answer 1

The correct option is A $-i$

$Z=(i{)}^{(i{)}^{\left(i\right)}}$

$i=e^{i\pi /2}$

$i^i=e^{i.\left(i\pi /2\right)}=e^{-\pi /2}$

$i^{i^i}=e^{i(-\pi /2)}⟹\cos \left(\pi /2\right)-i\sin \left(\pi /2\right)⟹0-i=-i$