Complex city

Calculus Level 3

If $\sqrt{-1}= i$ , then the expression below:

$\huge \sqrt[i]{\sqrt[.]{\sqrt[.]{\sqrt[.]{\sqrt[i]{\sqrt[i]{\sqrt[i]{i^i}^i}^i}^.}^.}^.}^i}$ :

Can also be written as:

e^{\frac{i \pi}{2}}

e^{\frac{\pi}{2}}

e^{-\frac{ \pi}{2}}

e^{ -\frac{i \pi}{2}}

1 solution

展豪張
May 12, 2016

The expression is simply just $i$ and $i=e^{\frac{i\pi}2}$