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Q. If $z$ is a complex number satisfying $z^{4}+z^{3}+2 z^{2}+z+1=0$, then the set of possible values of $|z|$ is

Complex Numbers and Quadratic Equations

Solution:

The given equation is $\left(z^{2}+z+1\right)\left(z^{2}+1\right)=0$
$\Rightarrow z=\pm i, \omega, \omega^{2}$;
where $\omega$ being an imaginary cube root of unity.
Thus $|z|=1$.