# If (x + iy)1/3 = (a + ib) then prove that = 4 (a2 – b2).

Given that, (x + iy)1/3 = (a + ib)

(x + iy) = (a + ib)3

(a + ib)3 = x + iy

a3 + (ib)3 + 3a2ib + 3ai2b2 = x + iy

a3 - ib3 + 3a2ib - 3ab2 = x + iy

a3 - 3ab2 + i(3a2b - b3) = x + iy

On equating real and imaginary parts, we get

x = a3 - 3ab2 and y = 3a2b - b3

Now ,

= a2 - 3b2 + 3a2 - b2

= 4a2 - 4b2

= 4(a2 - b2)

Hence,

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