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

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

If the points A(z),B(-z),C(1-z) are the vertices of an equilateral triangle ABC then Re(z) is

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 A(z_1), B(z_2), C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_3-2z_1)/(z_3-z_2)) is equal to

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

A(z_1),B(z_2),C(z_3) are the vertices a triangle ABC inscribed in the circle abs(z)=2 internal angle bosector of the angle A meet the circumference again at D(z_4) then prove z_4^2=z_2z_3

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

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