How do we know when to use theta=0 or 2pi in finding the 4th root of 100+0i

Question

How do we know when to use theta=0 or 2pi in finding the 4th root of 100+0i using DeMoivre's theorem

Answer 1

the basic solution will be, of course, square root of 10.  for this, theta = 0.

three other solutions will be √10(cis 90⁰

and √10(cis 180^o)

and √10(cis 270^o)

 

because fourth roots are involved, each successive angle is increased by ¼ of 360 degrees.