The complex fourth roots of 5-5sqrt3i

First convert the complex number to polar form

|5 - 5sqrt3i| = 25sqrt10

argument = arctan - sqrt3 = - pi/3

so 5 - 5sqrt3i = 25sqrt10 (cos (-pi/3) + i sin (-pi/3))

the angle is in the 4th quadrant so we could write it as 2pi-pi/3 = 5p/3

= 25sqrt10 (cos 5pi/3 + i sin 5pi/3)

Now if r (cosx + isin x) is a 5th root of 5-5sqrt3i then

r^5 (cos x + i sinx) ^5 = 25sqrt10 (cos 5pi/3 + i sin 5pi/3)

r^5 = 25sqrt10 and cos5x + i sin 5x = cos 5pi/3 + i sin 5pi/3

i have to go urgently so i have to leave it to you to finish this