Find the two square roots for the following complex number.

Question

Find the two square roots for the following complex number. Write your answers in standard form. (Enter your answers as a comma-separated list.)
−4 + 4i square root of 3

Answer 1

z = 4 [-1 + i√3] = 8 (cos θ + isinθ) =  where θ = 150^o

 

By DeMoivre's theorem, the two square roots of z are    2√2 (cos 75^o +  i sinθ 75^o)