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Harmonic Progression

If 8iz3 + 1...

Question

If $8 i z^{3} + 12 i z^{2} - 18 z + 27 i = 0$ , then the value of $| z |$ is

A

3 / 2

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B

2 / 3

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C

1

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D

3 / 4

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Solution

The correct option is A $3 / 2$
$8 i z^{3} + 12 i z^{2} - 18 z + 27 i = 0$

$= 4 i z^{2} (2 z - 3 i) - 9 (2 z - 3 i) = 0$

$= (2 z - 3 i) (4 i z^{2} - 9) = 0$

$= z = \frac{3 i}{2}$ & $z^{2} = \frac{9}{4 i}$

$∴ | z | = \frac{3}{2}$ & $| z |^{2} = \frac{9}{4}$

Hence $| z | = \frac{3}{2}$

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