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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

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${1, 2, 3}$

${1, 2, 3, 4}$

${1}$

${1, 2}$

answer is B.

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Detailed Solution

$z^{4} + z^{3} + 2 z^{2} + z + 1 = 0$

$z^{4} + z^{3} + z^{2} + z^{2} + z + 1 = 0$

$z^{2} (z^{2} + z + 1) + z^{2} + z + 1 = 0$

$(z^{2} + 1) (z^{2} + z + 1) = 0 1 + ω + ω^{2} = 0 a n d ω^{3} = 1 | z | = 1$

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