`(x+iy)^(1/3) =(a+ib)` then prove that `(x/a+y/b)=4(a^2-b^2)` – InterviewSolution

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1.	`(x+iy)^(1/3) =(a+ib)` then prove that `(x/a+y/b)=4(a^2-b^2)`
Answer» `(x+iy)=(a+ib)^(3)=a^(3)-ib^(3)+3iab(a+ib)` `rArr" "(x+iy)=(a^(3)-3ab^(2))+i(3a^(2)b-b^(3))` `rArr" "x=a^(3)-3ab^(2) and y = 3a^(2)b-b^(3)` `rArr" "((x)/(a)+(y)/(b))=(a^(2)-3b^(2))+(3a^(2)-b^(2))=4(a^(2)-b^(2))`.

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