`z_1, z_2 and z_3` are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that `z_2, z_1 and kz_3` are in G.P. where `k in R^+dot`

If z_1, z_2, z_3, z_4 represent the vertices of a rhombus in anticlockwise order, then

A(z_1),B(z_2),C(z_3) are the vertices of the triangle A B C (in anticlockwise). If /_A B C=pi//4 and A B=sqrt(2)(B C) , then prove that z_2=z_3+i(z_1-z_3)dot

if z_1, z_2, z_3 are the vertices pf an equilateral triangle inscribed in the circle absz=1 and z_1=i , then

On the Argand plane z_1, z_2a n dz_3 are respectively, the vertices of an isosceles triangle A B C with A C=B C and equal angles are thetadot If z_4 is the incenter of the triangle, then prove that (z_2-z_1)(z_3-z_1)=(1+sectheta)(z_4-z_1)^2dot

If z_(1) , z_(2) and z_(3) are the vertices of DeltaABC , which is not right angled triangle taken in anti-clock wise direction and z_(0) is the circumcentre, then ((z_(0)-z_(1))/(z_(0)-z_(2)))(sin2A)/(sin2B)+((z_(0)-z_(3))/(z_(0)-z_(2)))(sin2C)/(sin2B) is equal to

Complex numbers z_1 , z_2 , z_3 are the vertices A, B, C respectively of an isosceles right angled triangle with right angle at C and (z_1- z_2)^2 = k(z_1 - z_3) (z_3 -z_2) , then find k.

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i| = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals:

Let the complex numbers z_1,z_2 and z_3 be the vertices of an equilateral triangle let z_0 be the circumcentre of the triangle then prove that z_1^2+z_2^2+z_3^2=3z_0^2

If z_1, z_2, z_3 be the affixes of the vertices A, B and C of a triangle having centroid at G such that z = 0 is the mid point of AG then 4z_1 + z_2 + z_3 =

If A(z_1),B(z_2),C(z_3) and D(z_4) be the vertices of the square ABCD then