# Math Help - complex problem

1. ## complex problem

if mod(z1)=1 mod(z2)=2 mod(z3)=3 and mod(9z1z2+4z1z3+z2z3)=12 find the value of mod(z1+z2+z3)

i know mod(z1+z2+z3)<=mod(z1)+mod(z2)+mod(z3) but how to do this

2. Originally Posted by prasum
if mod(z1)=1 mod(z2)=2 mod(z3)=3 and mod(9z1z2+4z1z3+z2z3)=12 find the value of mod(z1+z2+z3)

i know mod(z1+z2+z3)<=mod(z1)+mod(z2)+mod(z3) but how to do this
Use the fact that $|z|^2 = z\overline{z}$. So $z_1\overline{z_1} = 1$, $z_2\overline{z_2} = 4$, $z_3\overline{z_3} = 9$, and $(9z_1z_2 + 4z_1z_3 + z_2z_3)(9\overline{z_1z_2} + 4\overline{z_1z_3} + \overline{z_2z_3}) = 144$. Multiply out that last one to get an expression for $z_1\overline{z_2} + z_1\overline{z_3} + z_2\overline{z_3}$. That will enable you to find $(z_1 + z_2 + z_3)(\overline{z_1} + \overline{z_2} + \overline{z_3}).$