\(\left\{{}\begin{matrix}z_1+z_2=m\\z_1z_2=2m-1\end{matrix}\right.\)
\(z_1^2+z_2^2=-10\)
\(\Leftrightarrow\left(z_1+z_2\right)^2-2z_1z_2=-10\)
\(\Leftrightarrow m^2-2\left(2m-1\right)=-10\)
\(\Leftrightarrow m^2-4m+12=0\)
\(\Rightarrow m=2\pm2\sqrt{2}i\)
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