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If x + iy = (a + ib)3, show that x/a + y/b = 4(a2 - b2)

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x + iy = (a + ib)3

x + iy = a3 + 3a2 bi + 3ab2 i2 + b3 i3 

x + iy = a3 + 3a2 bi – 3ab2 – b3 i ……[∵ i2 = -1, i3 = -i]

x + iy = (a3 – 3ab2 ) + (3a2b – b3 )i

Equating real and imaginary parts, we get

Alternate Method:

Equating real and imaginary parts, we get

x = a3 – 3ab2 and y = 3a2 b – b3

Consider

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