Kristina Mcclain

2022-02-01

How do you calculate $\sqrt[n]{i},\text{}n\in \mathbb{R}$ ?

Jaiden Conrad

Beginner2022-02-02Added 14 answers

Step 1

The polar form of$z=i$ is given by

$z=0+i1=\mathrm{cos}\left(\frac{\pi}{2}\right)+i\mathrm{sin}\left(\frac{\pi}{2}\right)={e}^{i\frac{\pi}{2}}$

Now according to De Moivres

The polar form of

Now according to De Moivres