Complex Disguise!

Algebra Level 4

Complex numbers z1z_1, z2z_2 and z3z_3 have the following properties.

  • z1=z2=z3=5|z_1|=|z_2|=|z_3|=5
  • z1+z2=0z_1+z_2=0

What is the value of (z3z1)(z3z1)+(z3z2)(z3z2)(z_3-z_1)(\overline{z_3-z_1})+(z_3-z_2)(\overline{z_3-z_2})?

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