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Q.
Points $z_1 \& z_2$ are adjacent vertices of a regular octagon. The vertex $z_3$ adjacent to $z_2\left(z_3 \neq z_1\right)$ is represented by :
Complex Numbers and Quadratic Equations
Solution:
$\frac{z_3-z_2}{z_2-z_1}= e ^{\pm i \frac{\pi}{4}}$
$\because \left|z_1-z_2\right|=\left|z_2-z_3\right|$
$\Rightarrow z_3=z_2+\left(\frac{1+i}{\sqrt{2}}\right)\left(z_2-z_1\right)$
