Question

If `(a^2 + 1)^2/(2a - i)` = x + iy, what is the value of x² + y²?

Answer 1

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)`.