Question

Please prove it and tell me the solution of above question given in the picture.⤴️​

Answer 1

Answer:

$x + iy = \frac{a - ib}{a + ib} \: \: \: \: \: \: - - - (1) \\ \\ x - iy = \frac{a + ib}{a - ib} \: \: \: \: \: - - - (2) \\ \\ multiply \: (1) \: \: and \: \: (2) \\ \\ (x + iy)(x - iy) = 1 \\ \\ {x}^{2} - {i}^{2} {y}^{2} = 1 \\ \\ {x}^{2} + {y}^{2} = 1 \: \: \: \: \: \: \: \: (hence \: \: proved)$