If (x+iy)^ 1/3 =a+ib where x,y,a,b R and i= -1 then x a - y b =

MHT CET 2022 Mathematics question

If where and then

Answer: (A)

Cube both sides: x+iy=(a+ib)^3=a^3+3a^2(ib)+3a(ib)^2+(ib)^3=(a^3-3ab^2)+i(3a^2b-b^3). Equating real and imaginary parts: and . Then and $

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Question ID VK-095823