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

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

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743