`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`

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

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

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

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

In A B C ,A(z_1),B(z_2),a n dC(z_3) are inscribed in the circle |z|=5. If H(z_H) be the orthocenrter of triangle A B C , then find z_H

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

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

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) 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

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