Question

BRAIN TESTER 03.

What is the value of :-

${iota}^{iota}$

Give answer with logic!

Answer 1

Here's it :

$using \: Euler's \: formula \: for \: relationship \: of \: complex \: exponential \: functions \: with \: trigonometric \: functions \: \\ {e}^{i \alpha } = \cos( \alpha ) + i \sin( \alpha ) and \: taking \: \alpha = \pi \div 2 \\ {e}^{i \frac{\pi}{2} } = 0 + 1 \times i = i \\ raising \: both \: sides \: to \: the \: power \: of \: i \: \\ {e}^{ {i}^{2} \frac{\pi}{2} } = {i}^{i} \\ since \: {i}^{2} = - 1 \\ {i}^{i} = {e}^{ \frac{ - \pi}{2} }$