If $z^{3} - {2 z}^{2} + 4 z - 8 = 0$ then

|z| = 1

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|z| = 2

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|z| = 3

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None of these

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Solution

The correct option is B |z| = 2
Given,

$z^{3} - 2 z^{2} + 4 z - 8 = 0$

$\Rightarrow (z - 2) (z^{2} + 4) = 0$

$\Rightarrow z - 2 = 0 : z = 2$

$\Rightarrow z^{2} + 4 = 0 : z = 2 i, z = - 2 i$

$∴ z = 2, z = 2 i, z = - 2 i$

$∴ | z | = 2$

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