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Q.
Number of solutions of the equation $\left|z\right|^{2}+7 \bar{z}=0$ is
Complex Numbers and Quadratic Equations
Solution:
Given $\left|z\right|^{2}+7 \bar{z}=0$
$\Rightarrow \, z \bar{z}+7 \bar{z}=0$
$\Rightarrow \, \bar{z}\left(z+7\right)=0$ Case (i) : $\bar{z}=0$,
$\therefore \, z=0=0+i0$ Case (ii): $z = - 7$
$\therefore \, z=-7+0i$
Hence there is only two solutions.