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

Question

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

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Henry Discussed

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

, find

4∣ z ∣^{2}

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Text solutionVerified

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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