If $i z^{3} + z^{2} - z + i = 0$ , then $| z |$ equals

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Solution

The correct option is D
1

We can write the given equation as
$z^{3} + \frac{1}{i} z^{2} - \frac{1}{i} z + 1 = 0$
$or z^{3} - i z^{2} + i z - i^{2} = 0 \Rightarrow z^{2} (z - i) + i (z - i) = 0 \Rightarrow (z^{2} + i) (z - i) = 0 \Rightarrow z^{2} = - i, z = i \Rightarrow | z |^{2} = | - i | and | z | = | i | \Rightarrow | z |^{2} = 1 and | z | = 1 \Rightarrow | z | = 1$

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