If - z -1 and z 1- z 3- z 2- z 3- z - i - z - i then z 1- z 2- z 3 will be vertices of aA- acute triangleB- obtuse triangleC- right triangle

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If | z |=1 an...

Question

If $| z | = 1$ and $\frac{z_{1} - z_{3}}{z_{2} - z_{3}} = \frac{z - i}{z + i}$ then $z_{1}, z_{2}, z_{3}$ will be vertices of a

acute triangle

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obtuse triangle

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right triangle

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Solution

The correct option is C right triangle
As $| z | = 1$ lies on circle, so I and -I are extremities of this circle.

So, arg $(\frac{z - i}{z + i})$ = $\pm \frac{π}{2}$ $\Rightarrow$ $\frac{z - i}{z + i}$ is purely imaginary
$\Rightarrow z_{1}, z_{2}, z_{3}$ represents vertices of right angled triangle

Suggest Corrections

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If |z|=1 and z1− z3z2− z3= z−iz+i then z1, z2, z3 will be vertices of a

The correct option is C right triangleAs |z|=1 lies on circle, so I and -I are extremities of this circle. So, arg (z−iz+i) = ±π2 ⇒ z−iz+i is purely imaginary ⇒z1,z2,z3 represents vertices of right angled triangle

If $| z | = 1$ and $\frac{z_{1} - z_{3}}{z_{2} - z_{3}} = \frac{z - i}{z + i}$ then $z_{1}, z_{2}, z_{3}$ will be vertices of a