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Question: If \|z\| = 2 an\(\frac{z_{1} - z_{3}}{z_{2} - z_{3}}\)= \(\frac{z - 2}{z + 2}\)then z<sub>1</sub>, z...

If |z| = 2 anz1−z3z2−z3\frac{z_{1} - z_{3}}{z_{2} - z_{3}}= z−2z+2\frac{z - 2}{z + 2}then z1, z2, z3 will be vertices of a/an-

A

Equilateral triangle

B

Acute angled triangle

C

Right angled triangle

D

Square

Answer

Right angled triangle

Explanation

Solution

Sol. arg (z−2z+2)\left( \frac{z - 2}{z + 2} \right) = ± π2\frac{\pi}{2}

Ž arg (z1−z3z2−z3)\left( \frac{z_{1} - z_{3}}{z_{2} - z_{3}} \right)= ±π2\frac{\pi}{2}

Ž z1, z2, z3 are vertices of a right angled triangle.