Question

If `8i z+12 z^2-18 z+27 i=0,t h e n` `|z|=3/2` b. `|z|=2/3` c.`|z|=1` d. `|z|=3/4`
A. `|z| = (3)/(2)`
B. `|z| = (3)/(4)`
C. `|z|=1`
D. `|z| = (3)/(4)`

Answer 1

Correct Answer - A
`8iz^(3)+12z^(2)-18z+27i=0`
or `4iz^(2)(2z-3i)-9(2z-3i)=0`
or `(2z-3i)(4iz^(2)-9)=0`
`rArr z =(3i)/(z)andz^(2)=(9)/(4i)`
`rArr |z|=(3)/(2)and|z^(2)|=(9)/(4)`
`rArr |z|=(3)/(2)`