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Question
If `(a^2 + 1)^2/(2a - i)` = x + iy, what is the value of x2 + y2?
Solution
Given that: `(a^2 + 1)^2/(2a - i)` = x + iy ......(i)
Taking conjugate on both sides
⇒ `(a^2 + 1)^2/(2a + i)` = x – iy ......(ii)
Multiplying equation (i) and (ii) we have
`((a^2 + 1)^2(a^2 + 1)^2)/((2a - i)(2a + i))` = x2 + y2
⇒ `(a^2 + 1)^4/(4a^2 - i^2)` = x2 + y2
⇒ `(a^2 + 1)^4/(4a^2 + 1)` = x2 + y2
Hence, the value of x2 + y2 = `(a^2 + 1)^4/(4a^2 + 1)`.
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