complex number

2-√2i=√[2^2+(-√2)^2]e^i(arctan(-√2/2))=√6 e^i(arctan(-1/√2))
(2-√2i)^5=(√6)^5 * e^5i(arctan(-1/√2))=36√6 e^5i(arctan(-1/√2))//


z^3+1=√3 i
z^3= -1+√3 i
z^3= √[(-1)^2+(√3)^2] e^i(arctan(-√3)
z^3=√4 e^(2πi/3)
z=(2)^(1/3) e^(2πi/9)
z=(2)^(1/3) ∠ (2π/9)

I don't know what form you want. Polar form can be present in various way
re^ix or r(cos x+i sin x) or r ∠ x or r cis x ...

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