Complex Numbers

Let $$z_1$$ = 18 + 83i, $$z_2$$ = 18 + 39i, ana $$z_3 $$= 78 + 99i. where i = $$\sqrt-1$$. Let z be a unique comlpex number with the properties that $$\dfrac{z_3 - z_1}{z_2 - z_1}$$ $$\cdot$$ $$\dfrac{z - z_2}{z - z_3}$$ is a real number and the imaginary part of the size z is the greatest possible.
If $${z}_{1}$$ and $${z}_{2}$$ are two non-zero complex numbers such that $$\left| \cfrac { { z }_{ 1 } }{ { z }_{ 2 } }  \right| =2$$ and $$arg(\left( { z }_{ 1 }{ z }_{ 2 } \right) =\cfrac { 3\pi  }{ 2 } $$, then $$\cfrac { \bar { { z }_{ 1 } }  }{ { z }_{ 2 } } $$ is equal