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  4. If z be a complex number satisfying z4 + z3 + 2z2 + z + 1 = 0, then |z| equals to

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Q. If $z$ be a complex number satisfying $z^4 + z^3 + 2z^2 + z + 1 = 0$, then $|z|$ equals to

Complex Numbers and Quadratic Equations

Solution:

Given $z^4 + z^3 + 2z^2 + z + 1 = 0$
$\Rightarrow (z^2 + z + 1)(z^2 + 1) = 0$
$\Rightarrow z = \omega, \omega^2, i, -i$
for each value of $z, |z| = 1$