If - z - -1 and z1- z3-z2- z3- z-i-z-i then z1- z2- z3 will be vertices of a

As | z |=1 lies on circle, so I and I are extremities of this circle. So, arg (z i/z+i) = ±π/2 ⇒ z i/z+i is purely imaginary ⇒ z_1, z_2, z_3 represents verti ...

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Standard XI

Mathematics

Properties of Modulus

If | z | =1 a...

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

equilateral triangle

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acute angled triangle

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obtuse angled triangle

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None of these

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Solution

The correct option is D None of these
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

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