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