My problems #1

Note that

$z^4 + z^3 + 2z^2 + z + 1 = z^4 + z^3 + z^2 + z^2 + z + 1 = (z^2 + 1)(z^2 + z + 1) = 0$

Case 1 : $z^2 + 1 = 0$

In this case, $z = \pm i$ .

$|\pm i| = 1$

Case 2 : $z^2 + z + 1 = 0$

In this case, $z = \dfrac {-1 \pm \sqrt {1^2 - 4 \cdot 1 \cdot 1}}{2 \cdot 1} = \dfrac {-1 \pm \sqrt {3} i}{2}$

$\mid \dfrac {-1 \pm \sqrt {3} i}{2} \mid = 1$

Therefore, $|z| = 1$ .

same way Bro