If A z 1- B z 2- C z 3 are the vertices of the triangle ABC such that z 1- z 2- z 3- z 2-1-2- i -2- then triangle ABC isA- IsoscelesB- EquilateralC- Right angledD- Obtuse angled

Given: (z_1 z_2)(z_3 z_2) = ( 1√(2) + nbsp; i√(2) ) ⇒|z_1 z_2z_3 z_2|=1 ⇒|z_1 z_2|=|z_3 z_2| ⇒ AB=BC and (z_1 z_2)(z_3 z_2)=e^iπ/4 ⇒∠ ABC=45^∘ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Geometrical Representation of a Complex Number

If A z 1, B z...

Question

If $A (z_{1}), B (z_{2}), C (z_{3})$ are the vertices of the triangle ABC such that $\frac{(z_{1} - z_{2})}{(z_{3} - z_{2})} = (\frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}})$ , then triangle $A B C$ is

Equilateral

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

Right angled

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

Isosceles

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

Obtuse angled

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

Open in App

Solution

The correct option is C Isosceles
Given $\frac{(z_{1} - z_{2})}{(z_{3} - z_{2})} = (\frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}})$
$\Rightarrow ∣ ∣ ∣ \frac{z_{1} - z_{2}}{z_{3} - z_{2}} ∣ ∣ ∣ = 1 \Rightarrow | z_{1} - z_{2} | = | z_{3} - z_{2} | \Rightarrow A B = B C$
and $\frac{(z_{1} - z_{2})}{(z_{3} - z_{2})} = e^{i π / 4}$
$\Rightarrow ∠ A B C = 45^{\circ}$

Suggest Corrections

Similar questions

Q. If

A (z_{1}), B (z_{2}), C (z_{3})

are the vertices of the triangle ABC such that

\frac{(z_{1} - z_{2})}{(z_{3} - z_{2})} = (\frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}})

, then triangle

A B C

A (z_{1}), B (z_{2}), C (z_{3})

are the vertices of the triangle

A B C

(in anticlockwise order). If

∠ A B C = \frac{π}{4}

and

A B = \sqrt{2} (B C)

, then

Q. The complex numbers

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

satisfying

\frac{z_{1} - z_{3}}{z_{2} - z_{3}} = \frac{1 - i \sqrt{3}}{2}

are the vertices of a vertices of a triangle which is

Q. If three complex numbers

z_{1}, z_{2}

and

z_{3}

satisfy

\frac{z_{1} - z_{3}}{z_{2} - z_{3}} = \frac{1 - i \sqrt{3}}{2}

, then the triangle formed by

z_{1}, z_{2}

and

z_{3}

If A(z₁), B(z₂) and C(z₃) are three points in the argand plane where

| z₁+ z₂ | = | |z₁| - |z₂| | and | (1 - i)z₁+ iz₃ | = | z₁| + | z₃- z₁| ,

where i = √( -1) then

(a) A, B and C lie on a fixed circle with centre (z₂+ z₃)/2

(b) A, B and C are collinear points

(d) ABC form an obtuse angle triangle

Join BYJU'S Learning Program

Explore more

Geometrical Representation of a Complex Number

Standard XII Mathematics

Join BYJU'S Learning Program

If A(z1),B(z2),C(z3) are the vertices of the triangle ABC such that (z1−z2)(z3−z2)=(1√2+i√2), then triangle ABC is

The correct option is C Isosceles Given (z1−z2)(z3−z2)=(1√2+i√2) ⇒∣∣∣z1−z2z3−z2∣∣∣=1⇒|z1−z2|=|z3−z2|⇒AB=BC and (z1−z2)(z3−z2)=eiπ/4 ⇒∠ABC=45∘

If $A (z_{1}), B (z_{2}), C (z_{3})$ are the vertices of the triangle ABC such that $\frac{(z_{1} - z_{2})}{(z_{3} - z_{2})} = (\frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}})$ , then triangle $A B C$ is