# Complex Number -A problem on conjugate

|$z_1$|=2,|$z_2$|=3,|$z_3$|=4 and |$2z_1+3z_2+4z_3$|=9 then the absolute value of $8z_2z_3+27z_3z_1+64z_1z_2$ must be equal to?

($z_1,z_2,z_3$ are complex numbers)

I tried manipulating with the conjugates and stuff...but not being able to figure out the right technique to solve..help please!!

HINT: Try to multiply the expression $|2\bar{z_1}+3\bar{z_2}+4\bar{z_3}|$ by the product $|z_1z_2z_3|$. What is the value of $|2\bar{z_1}+3\bar{z_2}+4\bar{z_3}|$?
Given expression equals $|z_1z_2z_3||8/z_1+27/z_2+64/z_3|$ =$|z1||z2||z3||2z_1+3z_2+4z_3|$=2.3.4.9=216