Mathematics

Problem

Let

z_1 = 10 + 6i

z_2 = 4 + 6i

, where i =

\sqrt{-1}

. If

z

is a complex number, such that the argument of

(z - z_1)/(z - z_2)

\pi/4

, then prove that

|z - 7 - 9i| = 3\sqrt{2}