Complex Arithmetic/Examples

Example: $3 \paren {\dfrac {1 + i} {1 - i} }^2 - 2 \paren {\dfrac {1 - i} {1 + i} }^3$
Let $z_1 = 2 + i$, $z_2 = 3 - 2 i$ and $z^3 = -\dfrac 1 2 + \dfrac {\sqrt 3} 2 i$.

Example: $\cmod {\dfrac {2 z_2 + z_1 - 5 - 1} {2 z_1 - z_2 + 3 - 1} }^2$
Let $z_1 = 1 - i$, $z_2 = -2 + 4 i$ and $z_3 = \sqrt 3 - 2 i$.