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If $(x + i y)^{1 / 3} = a + i b,$ then $\frac{x}{a} + \frac{y}{b}$ equals

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4(a2-b2)

2(a2-b2)

2(a2+b2)

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detailed solution

Correct option is A

(x+iy)1/3=a+ib⇒ x+iy=(a+ib)3=a3+3a2(ib)+3a(ib)2+(ib)3⇒ x+iy=a3−3ab2+3a2b−b3iEquating real and imaginary parts, we get x=a3-3ab2 and y=3a2b-b3⇒ xa=a2-3b2 and xb=3a2-b2.Thus, xa+yb=4a2-4b2=4(a2-b2)

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If (x+iy)1/3=a+ib, then xa+ybequals

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If $(x + i y)^{1 / 3} = a + i b,$ then $\frac{x}{a} + \frac{y}{b}$ equals