Question

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

• A. $|z|=\frac{3}{2}$
• B. $|z|=\frac{2}{3}$
• C. $|z|=1$
• D. $|z|=\frac{3}{4}$

Answer 1

Answer: (A)

$8 i z^3+12 z^2-18 z+27 i =0 $
$\Rightarrow 8 i z^3-12 i^2 z^2-18 z+27 i =0$
$\Rightarrow 4 i z^2(2 z-3 i)-9(2 z-3 i) =0$
$\Rightarrow \left(4 i z^2-9\right)(2 z-3 i)=0 $
$\Rightarrow z^2=\frac{9}{4 i} \text { or } z=\frac{3 i}{2}$
In any case $|z|=3 / 2$.