# If (x + iy)3 = (u + iv) then prove that = 4 (x2 – y2).

Given that, (x + iy)3 = (u + iv)

x3 + (iy)3 + 3x2iy + 3xi2y2 = u + iv

x3 - iy3 + 3x2iy - 3xy2 = u + iv

x3 - 3xy2 + i(3x2y - y3) = u + iv

On equating real and imaginary parts, we get

U = x3 - 3xy2 and v = 3x2y - y3

Now ,

= x2 - 3y2 + 3x2 - y2

= 4x2 - 4y2

= 4(x2 - y2)

Hence,

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