ISRO 2015- Complex Numbers [EE]

Question

If x = √ -1. then the value of x x is

(a) e- π /2

(b) x

(c) e π /2

(d) 1

Answer 1

$\begin{align*} x &= i\\ &= cos\frac{\pi}{2} + i.sin\frac{\pi}{2}\\ &= e^{i.\frac{\pi}{2}}\\ x^x& = (e^{i.\frac{\pi}{2}})^i\\ & = e^{-\frac{\pi}{2}} \end{align*}$

Hence, A is the answer.

Answer 2

A is the answer