If $a 0, a \in R, z=a+2 i$ and $z|z|-a z+1=0$ then

Question

If $a > 0, a \in R, z=a+2 i$ and $z|z|-a z+1=0$ then, $z$ is always a positive real number, $z$ is always a negative real number, $z$ is purely imaginary number, such a complex z does not exist

MARKS App · Accepted Answer

Putting $z=a+2 i$ in the given equation and comparing imaginary parts, we get $\mathrm{a}^2+4=\mathrm{a}^2$, which is not possible.

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