If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3|=12 then |z1 + z2 + z3| = ___

given conditions are:

• |z1| = 1
• |z2| = 2
• |z3| = 3
• |9z1z2 + 4z1z3 + z2z3| = 12

We need to find |z1 + z2 + z3|.

Step-by-step solution:

We are given the magnitudes of the complex numbers z1, z2, and z3, as well as the magnitude of the expression 9z1z2 + 4z1z3 + z2z3.

The strategy here is to work with the magnitudes of complex numbers and their relationships. We already know that:

• |z1| = 1
• |z2| = 2
• |z3| = 3

Also, we are given the magnitude |9z1z2 + 4z1z3 + z2z3| = 12.

Using the triangle inequality and the properties of complex numbers, it can be shown that:

|z1 + z2 + z3| = 2

Thus, the answer is 2.