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

| ω |

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\frac{3}{4}

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| \pm i |

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None of these

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Solution

The correct options are
A $| ω |$
C $| \pm i |$
$(z^{4} + z^{3} + z^{2}) + (z^{2} + z + 1) = 0$
$z^{2} (z^{2} + z + 1) + 1 (z^{2} + z + 1) = 0$
$(z^{2} + 1) (z^{2} + z + 1) = 0$
Hence
$z^{2} + 1 = 0$
$z = \pm i$
and
$z^{2} + z + 1 = 0$
$z = w, w^{2}$
Hence
$| z |$
$= | i |$
$= | w |$
$= | w^{2} |$
$= 1$

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