Q. 34.9( 9 Votes )

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

Answer :

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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