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If 8i z+12 z^2-18 z+27 i=0,t h e n |z|=...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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)`
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