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Q.
If $\frac{z_{3}-z_{1}}{z_{3}-z_{2}}=i$, then points $z_{1}, z_{2}$ and $z_{3}$
Complex Numbers and Quadratic Equations
Solution:
$\frac{z_{3}-z_{1}}{z_{3}-z_{2}}=i$
$\therefore \left|\frac{z_{3}-z_{1}}{z_{3}-z_{2}}\right|=1$
$\therefore \left|z_{3}-z_{1}\right|=\left|z_{3}-z_{2}\right|$
Also $\arg \left(\frac{z_{3}-z_{1}}{z_{3}-z_{2}}\right)=\frac{\pi}{2}$
$\therefore$ angle at vertex $z_{3}$ is $90^{\circ}$
Hence triangle is isosceles right angled.