### Complex Numbers

goals
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