Which of the following is a complex number where a ≠ 0 and b ≠ 0? A -7 B Pi C 4 + 9i D 2+ sqrt3

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Find the three cube roots of z=−2+2iz=−2+2i

complex-numbers

nnth roots of a complex number:

For a positive integer nn, the complex number z=r(cos(θ)+isin(θ))z=r(cos⁡(θ)+isin⁡(θ)) has exactly nn distinct nnth roots given by

r√n(cos(θ+2πkn)+isin(θ+2πkn))rn(cos⁡(θ+2πkn)+isin⁡(θ+2πkn))

where k=0,1,2,...,n−1k=0,1,2,...,n−1

Find the three cube roots of z=−2+2iz=−2+2i

r=(−2)2+22−−−−−−