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