Answer:
2(cos135° + isin135°)
Step-by-step explanation:
z^6 = 64i
We need to change i to polar form
cos (90) + isin (90) = i
x^6 = 64 cos (90) + isin (90)
Now we need to take the sixth root of each side
(x^6) ^ 1/6 = ((64)( cos (90) + isin (90)) ^ 1/6
(x^6) ^ 1/6 = ((64) ^ 1/6 * cos (90) + isin (90)) ^ 1/6
(x^6) ^ 1/6 = 2( * cos (90) + isin (90)) ^ 1/6
We we take the roots of the trig functions, we have 6 roots
360/n means the roots are 60 degrees are apart
take 90 /6 = 15 degrees
The first root is at 2 (cos (15) + isin (15))
The second root is at 2 (cos (15+60) + isin (15+60))
2 (cos (75) + isin (75))
The third root is at 2 (cos (75+60) + isin (75+60))
2 (cos (135) + isin (135))
and so on
