# Complex Disguise!

Algebra Level 4

$$z_1$$, $$z_2$$ and $$z_3$$ are complex numbers with the following properties.

a. $$|z_1|=|z_2|=|z_3|=5$$

b. $$z_1+z_2=0$$

What is the value of $$(z_3-z_1)(\overline{z_3-z_1})+(z_3-z_2)(\overline{z_3-z_2})$$?

×