For three complex numbers we have:
$|z_1|=1$ ,$|z_2|=2$ ,$|z_3|=3$
$|9z_1z_2 + 4z_1z_3 + z_2z_3|=12$
Then find value of $|z_1 + z_2 + z_3|$
I took $z_1=1(\cos A+i\sin A),z_2=2(\cos B+i\sin B),z_3=3(\cos A+i\sin A)$ but it doesn't help much. Any hint?
What I could see is that $|9z_1z_2 + 4z_1z_3 + z_2z_3|=12$ can be rewritten as
$||z_3|^2z_1z_2 +|z_2|^2z_1z_3 + |z_1|^2 z_2z_3|=12$ , but not so sure if it is useful.