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

\frac{2 i}{3}

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\frac{4 i}{9}

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\frac{2}{3}

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\frac{4}{9}

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Solution

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

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

$⟹ z = \frac{2}{3} i$ or $z^{2} = - \frac{4}{9} i$

$⟹ | z | = \frac{2}{3}$

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Similar questions

27 i z^{3} + 18 z^{2} - 8 i = 0,

| z | =

8 i z^{3} + 12 z^{2} - 18 z + 27 i = 0

4 | z |^{2}

(2 + 8 i) (1 - 4 i) - (3 - 2 i) (6 + 4 i)

: i = \sqrt{- 1}

9 + i, 4 + 13 i, - 8 + 8 i, - 3 - 4 i

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i

z_{1}, z_{2}

z_{3}

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