4 Find all 3 cube roots of z You may express your answers in

4. Find all 3 cube roots of z. You may express your answers in trig form.

Solution

z = 4 sqrt 3 - 4i

z^3 = 4 sqrt 3 - 4i

r = 4

theta = -pi/6

so we have

1st root = 4 ( cos (-pi/18) - i sin (-pi/18 ))

2nd root = 4 ( cos (-11pi/18) - i sin (-11pi/18))

3rd root = 4 ( cos (-23pi/18 ) - i sin (-23pi/18))