Question

Find (–1 –i sqrt(3))^10 .Express in rectangular form.

Answer 1

z = - 1 - i√3
x = - 1, y = -√3
r = |z| = √ ( -1)² + (-√3)² = √( 1 + 3 )= √4 = 2
Ф = arc tan ( -√3/-1 ) = arc tan (√3 ) = 60° = π/3
r ^n ( cos nФ + i sinФ ) = 2^10 ( cos (10π/3) + i sin (10π/3) )=
= 2^10( -1/2 - i √3/2 ) = 2^9( - 1 - i √3 )