Let \(n\) denote the number of solutions of the equation \(z^2+3 \bar{z}=0\), where \(z\) is a complex number. Then the …

Let \(n\) denote the number of solutions of the equation \(z^2+3 \bar{z}=0\), where \(z\) is a complex number. Then the value of \(\sum^{\infty} \frac{1}{n^k}\) is equal to:

[JEE Main 2021, 22 Jul (Shift 2)]