Complex Disguise!

Algebra Level 4

Complex numbers \(z_1\), \(z_2\) and \(z_3\) have the following properties.

  • \(|z_1|=|z_2|=|z_3|=5\)
  • \(z_1+z_2=0\)

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

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