Question

Find the cube roots of 125(cos 288° + i sin 288°).

So I know the answers are:
5 (cos 96 + i sin 96)
5(cos 216 + i sin 216 )
5 (cos 336 + i sin 336)
but I don't know how people found these answers. If you could possibly explain in like the easiest way.

Answer 1

wait what does this mean tho?

Answer 2

z = rcos(theta + i * sin(theta))
you are given
125(cos 288° + i sin 288°).
therefore your r value is 125, your theta is 288, your n value is 3 since you want a cubic root
plug these into the formula.

Answer 3

for the n value where does that go into the formula?

Answer 4

Look where it says “n” on the prove line

Answer 5

oh my bad... i was looking at the different formula. but my calc keeps saying it can't solve this. Is that normal?

Answer 6

you don't need a calculator for this

start with k = 0, r = 125, n = 3, theta = 288, plug these into the formula and simplify