Home
Class 12
MATHS
If |z|=2a n d(z1-z3)/(z2-z3)=(z-2)/(z+3)...

If `|z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+3)` , then prove that `z_1, z_2, z_3` are vertices of a right angled triangle.

Text Solution

Verified by Experts

For circe, `|z|=2`, points z = 2 and z=- 2 are end points of diameter.
`rArr arg ((z-2)/(z+2)) = pm(pi)/(2)`
`rArr arg ((z_(1)-z_(3))/(z_(2)-z_(3))) = (pi)/(2)`
Therefore, `z_(1),z_(2)` and `z_(3)` are the vertices of a right angled triangle.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.11|6 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Single)|89 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.9|8 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

If |z|=2and(z_(1)-z_(3))/(z_(2)-z_(3))=(z-2)/(z+2), then prove that z_(1),z_(2),z_(3) are vertices of a right angled triangle.

If |z_(1)|=|z_(2)|=|z_(3)| and z_(1)+z_(2)+z_(3)=0 , then z_(1),z_(2),z_(3) are vertices of

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

The complex numbers z_1 z_2 and z3 satisfying (z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2 are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

The complex number z_(1),z_(2) and z_(3) satisfying (z_(1)-z_(3))/(z_(2)-z_(3))=(1-i sqrt(3))/(2) are the vertices of a triangle which is :

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then

The complex numbers z_(1),z_(2),z_(3) stisfying (z_(2)=z_(3))=(1+i)(z_(1)-z_(3)).where i=sqrt(-1), are vertices of a triangle which is