Question

If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`

Answer 1

`x – iy = sqrt((a-ib)/(c - id))` ...... (1)

In place of i - on writing, i

`x – iy = sqrt((a-ib)/(c - id))`

On multiplying equations (1) and (2), we get

`(x - iy)(x + iy) = sqrt((a - ib)/(c  - id)) xx sqrt((a + ib)/(c  + id))`

= or `x^2 - i^2y^2 = sqrt((a^2 - i^2 b^2)/(c^2  - i^2 d^2))`

∴ `x^2 + y^2 = sqrt((a^2 + b^2)/(c^2 + d^2)`

On squaring both sides,

`(x^2 + y^2)^2 = (a^2 + b^2)/(c^2 + d^2)`