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.

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 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.

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.

If z_1, z_2, z_3 are complex numbers such that (2//z_1)=(1//z_2)+(1//z_3), then show that the points represented by z_1, z_2()_, z_3 lie one a circle passing through e origin.

If z_1, z_2, z_3 are complex numbers such that (2//z_1)=(1//z_2)+(1//z_3), then show that the points represented by z_1, z_2, z_3 lie one a circle passing through the origin.

If z_1 and z_2 are complex numbers such that |z_1-z_2|=|z_1+z_2| and A and B re the points representing z_1 and z_2 then the orthocentre of /_\OAB, where O is the origin is (A) (z_1+z_2)/2 (B) 0 (C) (z_1-z_2)/2 (D) none of these

Prove that the complex numbers z_(1) and z_(2) and the origin form an isosceles triangle with vertical angle (2pi)/(3),ifz_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0.

If 2z_1-3z_2 + z_3=0 , then z_1, z_2 and z_3 are represented by

Prove that the complex numbers z_(1),z_(2) and the origin form an equilateral triangle only if z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0 .

If |z|=2a n d(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.