How do you find all the values of the following complex numbers?

Question

a) i^(1/4)

b) 1^(1/5)

c) (−16)^(1/4)

Answer 1

Let's work through the first one. Replace i with e^(i*pi/2).

i^(1/4) = [e^(i*pi/2)]^(1/4) = e^(i*pi/8) = cos(pi/8) + i*sin(pi/8).

It turns out that you can find the exact values (in terms of roots) of cos(pi/8) and sin (pi/8).

That is a challenge for you.