If \( i z^{3}+z^{2}-z+i=0 \), then \( |z| \) is equal to

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If \( i z^{3}+z^{2}-z+i=0 \), then \( |z| \) is equal to

MathematicsComplex NumberJEE Main

Solution:

2469 Upvotes Verified Answer

The correct answer is: 1

Given, ${iz}^{3} + z^{2} - z + i = 0$
$z^{3} + \frac{1}{i} z^{2} - \frac{z}{i} + 1 = 0$
$\Rightarrow z^{3} - {iz}^{2} + iz + 1 = 0$
$\Rightarrow z^{2} (z - i) + i (z - i) = 0$
$\Rightarrow (z - i) (z^{2} + i) = 0$
$\Rightarrow z = i$ or $z^{2} = - i$
Hence, $| z | = 1$

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