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 ...

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

acute angled triangle

No worries! We‘ve got your back. Try BYJU‘S free classes today!

obtuse angled triangle

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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

Suggest Corrections

Similar questions

Q. 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

Q. 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

Q. If

| z | = 2

and

\frac{z_{1} - z_{3}}{z_{2} - z_{3}} = \frac{z - 2}{z + 2}

Then show that

z_{1}, z_{2}, z_{3}

are vertices of a right-angled triangle.

Let $z_{1}, z_{2}, z_{3}$ are the vertices of an equilateral triangle inscribed in the circle $| z |$ = 2. If $z_{1}, z_{2}, z_{3}$ are in the clockwise sense and $z_{1}$ = $1 + i \sqrt{3}$ , then: