Home
Class 12
MATHS
If theta is real and z1, z2 are connecte...

If `theta` is real and `z_1, z_2` are connected by `z1 2+z2 2+2z_1z_2costheta=0,` then prove that the triangle formed by vertices `O ,z_1a n dz_2` is isosceles.

Text Solution

AI Generated Solution

To prove that the triangle formed by the vertices \( O, z_1, \) and \( z_2 \) is isosceles given the equation \( z_1^2 + z_2^2 + 2z_1z_2 \cos \theta = 0 \), we can follow these steps: ### Step 1: Rewrite the Given Equation We start with the given equation: \[ z_1^2 + z_2^2 + 2z_1z_2 \cos \theta = 0 \] ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|60 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

If theta is real and z_1, z_2 are connected by z_1 2+z_2 2+2z_1z_2costheta=0, then prove that the triangle formed by vertices O ,z_1a n dz_2 is isosceles.

If z_1^2+z_2^2-2z_1.z_2.costheta= 0 prove that the points represented by z_1, z_2 , and the origin form an isosceles triangle.

The triangle with vertices at the point z_1z_2,(1-i)z_1+i z_2 is

If |z_1|=|z_2|=|z_3|=1 and z_1+z_2+z_3=0 then the area of the triangle whose vertices are z_1, z_2, z_3 is 3sqrt(3)//4 b. sqrt(3)//4 c. 1 d. 2

If z + 1/z = 2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tanntheta|

Let z_1, z_2, z_3 be the three nonzero complex numbers such that z_2!=1,a=|z_1|,b=|z_2|a n d c=|z_3|dot Let |a b c b c a c a b|=0 a r g(z_3)/(z_2)=a r g((z_3-z_1)/(z_2-z_1))^2 orthocentre of triangle formed by z_1, z_2, z_3, i sz_1+z_2+z_3 if triangle formed by z_1, z_2, z_3 is equilateral, then its area is (3sqrt(3))/2|z_1|^2 if triangle formed by z_1, z_2, z_3 is equilateral, then z_1+z_2+z_3=0

If z_0 is the circumcenter of an equilateral triangle with vertices z_1, z_2, z_3 then z_1^2+z_2^2+z_3^2 is equal to

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

if |z_1+z_2|=|z_1|+|z_2|, then prove that a r g(z_1)=a r g(z_2) if |z_1-z_2|=|z_1|+|z_2|, then prove that a r g(z_1)=a r g(z_2)=pi

z_1a n dz_2 are the roots of 3z^2+3z+b=0. if O(0),(z_1),(z_2) form an equilateral triangle, then find the value of bdot