Hello, Harshal!
I assume you're familiar with DeMoivre's Theorem . . .
Find the sixth roots of (12 + 5i)
Convert to polar form: .12 + 5i .= .13(cosθ + i·sinθ), .where θ = arctan(5/12) .*
Then: .(12 + 5y)^(1/6) . = . 13^(1/6) (cos[θ + 2kπ)/6] + i·sin[(θ + 2kπ)/6])
. . Evaluate for k = 0, 1, 2, 3, 4, 5
*
Edit: corrected my typo.
. . . .Thanks for pointing it out, Captain.