Find the complex number `omega` satisfying the equation `z^3-8i` and lying in the second quadrant on the complex plane.

Explanation

`z^(3) = 8i`
`or z^(3) = - 8i^(3)`
`or((z)/(-2i))^(3) = 1` or `omega` or `omega^(2)`
`rArr z = -2i or -2iomega or - 2iomega^(2)`
`rArr z=-2i or 2i((-1+sqrt(3i))/(2)) or -2i ((-1-sqrt(3))/(2))`
Hence, `z= - 2i or i + sqrt(3) or i - sqrt(3)` out of which `i- sqrt(3)` lies in the second quadrant.