Question

Find the fifth roots of 243(cos 240° + i sin 240°).

Answer 1

I solved it. Here's some steps for future references.

First, write the number in trig form:
r^5 = 243 and theta = 240 degrees.

Now, I must take the 5th root of 243 which is 3.
So, one root is "3".

Apply deMoivre's Theorem and divide 240 degrees by 5 and add (k+360/3) with k going from 0 to 2:
(240/5)+(0+360/3) = 168
(240/5)+(1+360/3) = 169
(240/5)+(2+360/3) = 170

Your roots are: 3, 168, 169, 170