# If $(x+iy)^{\large\frac{1}{3}}=a+ib$ then $\large\frac{x}{a}+\frac{y}{b}$ equals

$\begin{array}{1 1}(A)\;2(a^2+b^2)&(B)\;2(a^2-b^2)\\(C)\;4(a^2+b^2)&(D)\;4(a^2-b^2)\end{array}$

$(x+iy)^{\large\frac{1}{3}}=a+ib$
$\Rightarrow x+iy=(a+ib)^3=a^3+3a^2(ib)+3a(ib)^2+(ib)^3$
$\Rightarrow x+iy=(a^3-3ab^2)+(3a^2b-b^3)i$
$\Rightarrow x=a^3-3ab^2$,$y=3a^2b-b^3$
$\Rightarrow \large\frac{x}{a}$$=a^2-3ab^2,\large\frac{y}{b}$$=3a^2-b^2$