Question

Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form

(a + bi.) [(Sqrt(3)-i]^-10

Answer 1

√3 - i = 2e^(5πi/6)

(2e^(5πi/6))^-10 = 2^-10 * e^(-25πi/3)

= 2^-10 * (cos(-25π/3) + isin(-25π/3))

= 2^-10* (1/2 - i(√3/2))