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Modulus of a Complex Number

Question

If $i z^{3} + z^{2} - z + i = 0$ , then $| z | = 1$ . If this is true enter 1, else enter 0.

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Solution

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$i z^{3} + z^{2} - z + i = 0$
$\Rightarrow i z^{2} (z - i) - (z - i) = 0$
$\Rightarrow (z - i) (i z^{2} - 1) = 0$
$\Rightarrow z = 1$
Therefore, $| z | = 1$
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