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If $\frac{(a^2+1)^2}{2a-i}=x+iy$ ........(i)

Taking conjugate on both sides $\frac{a^2+1}{2a+i}^2=x-iy...............(ii)$

Multiplying eqn iand iiwe have $\frac{\left (a^2+1 \right )^2\left (a^2+1 \right )^2}{\left (2a-i \right )\left (2a+i \right )}=x^2+y^2$

$\frac{\left (a^2+1 \right )^4}{\left (4a^2-i^2 \right )}=x^2+y^2=\frac{\left (a^2+1 \right )^4}{\left (4a^2+1 \right )}$

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