Find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.

Let . Then

lies in the second quadrant, so

So we have

and the fourth roots of are

where . In particular, they are

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180