If $8 i z^{3} + 12 z^{2} - 18 z + 27 i = 0$ , find $4 | z |^{2}$ .

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Solution

$8 i z^{3} + 12 z^{2} - 18 z + 27 i = 0$
$\Rightarrow 4 z^{2} (2 i z + 3) + 9 i (2 i z + 3) = 0$
$\Rightarrow (2 i z + 3) (4 z^{2} + 9 i) = 0$
$\Rightarrow z = \frac{3 i}{4}$
Therefore, $4 | z |^{2} = 9$
Ans: 9

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