Question

Find the cube roots of unity in standard form (a+bi). Use exact values.

Answer 1

Every non-zero complex number has three cube roots. In general, any non-integer exponent, like

1

3

here, gives rise to multiple values. The way we find them is by multiplying

z

by 1 before exponentiating. We write

1

using Euler's Identity to the

2

k

power for integer

k

. That's