Let $z \in C$ be such that $\frac{z^2+3 i}{z-2+i}=2+3 i$. Then the sum of all possible values of $z^2$ is

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Aicharya · Accepted Answer

$z^2+3 i=z(2+3 i)-7-4 i$ $\mathrm{z}^2-\mathrm{z}(2+3 \mathrm{i})+7+7 \mathrm{i}=0$ $\begin{aligned} & z_1^2+z_2^2=\left(z_1+z_2ight)^2-2 z_1 z_2 \ & =4-9+12 i-14-14 i \ & =-19-2 i \end{aligned}$

Let $z \in C$ be such that $\frac{z^2+3 i}{z-2+i}=2+3 i$. Then the sum of all possible values of $z^2$ is

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