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 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 z_(1)^(2)+z_(2)^(2)+2z_(1)z_(2)cos theta=0, then prove that the triangle formed by vertices O,z_(1)andz_(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.

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 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 |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

8.If z_(1)^(2)+z_(2)^(2)+2zz_(2)*cos theta=0 prove that the points represented by z_(1),z_(2), and the origin form an isosceles triangle.

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

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

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