Magic of Complex Numbers#1

Algebra Level 2

If $e^{πi} + 1=0$ and $i=\sqrt{-1}$ , then $i^i = ?$

Notes:

If you haven't seen $i$ before, then also you can solve this problem using ordinary algebra.
Many properties that are true for real numbers are also true for numbers with symbol $i$ .

e^{2π}

e^{-0.5π}

e^{-π}

e^{0.5π}

e^{π}

1 solution

Vaibhav Priyadarshi
May 18, 2018

$e^{πi}=-1$ , $i^i=(-1)^{0.5i}=e^{πi\times0.5i}=e^{0.5πi^{2}}=e^{-0.5π}$