Question

prove that:\ [\arg \left(\frac{z_{3}-z_{2}}{z_{3}-z_{1}}\right) = \frac{1}{2} \arg\left(\frac{z_{2}}{z_{1}}\right)]\

if \[\|z_{1}|=|z_{2}|=|z_{3}|]\

Answer 1

\[\arg \frac{z_{3}-z_{2}}{z_{3}-z_{1}}=\frac{1}{2}\arg \frac{z_2}{z_1}\]

Answer 2

if: \[|z_{1}|=|z_{2}|=|z_{3}|\]

Answer 3

\[ \arg\left( z_1 \over z_2\right) = \arg (z_1) - \arg (z_2) \]