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_1^2+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_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

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∣