If 8iz3 + 12z2 - 18z + 27i = 0, then

8iz3+12z2−18z+27i=0or 4iz2(2z−3i)−9(2z−3i)=0or (2z−3i)4iz2−9=0⇒ z=3i2 and z2=94i⇒ |z|=32 and z2=94⇒ |z|=32

If 8iz3 + 12z2 - 18z + 27i = 0, then

8iz3+12z2−18z+27i=0or 4iz2(2z−3i)−9(2z−3i)=0or (2z−3i)4iz2−9=0⇒ z=3i2 and z2=94i⇒ |z|=32 and z2=94⇒ |z|=32

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If 8iz³ + 12z² - 18z + 27i = 0, then

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

$| z | = 1$

$| z | = \frac{3}{4}$

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

answer is A.

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Detailed Solution

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

$\begin{array}{l} or 4 {iz}^{2} (2 z - 3 i) - 9 (2 z - 3 i) = 0 \\ or (2 z - 3 i) (4 {iz}^{2} - 9) = 0 \end{array}$

$\begin{array}{l} \Rightarrow z = \frac{3 i}{2} and z^{2} = \frac{9}{4 i} \\ \Rightarrow | z | = \frac{3}{2} and |z^{2}| = \frac{9}{4} \\ \Rightarrow | z | = \frac{3}{2} \end{array}$

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If 8iz³ + 12z² - 18z + 27i = 0, then