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Question: If x + iy = \(\frac{u + iv}{u - iv}\), then x<sup>2</sup> + y<sup>2</sup> =...

If x + iy = u+ivu−iv\frac{u + iv}{u - iv}, then x2 + y2 =

A

1

B

–1

C

0

D

None of these

Answer

1

Explanation

Solution

Sol. Taking modulus on both sides x2 + y2

= ∣U+iV∣∣U−iV∣=U2+V2U2+V2\frac{|U + iV|}{|U - iV|} = \frac{U^{2} + V^{2}}{U^{2} + V^{2}}= 1