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 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 vertices of an acute-angled triangle are A(z_1),B(z_2),a n dC(z_3)dot If the origin O is the orthocentre of the triangle, then prove that z_1 bar z _2+ bar z _1z_2=z_2 bar z _3+ bar z _2z_3=z_3 bar z _1+ bar z _3z_1

Consider the circle |z|=r in the Argand plane, which is in fact the incircle of triangle A B Cdot If contact points opposite to the vertices A ,B ,C are A_1(z_1),B(z_2) a n d C_1(z_3) , obtain the complex numbers associated with the vertices A ,B ,C in terms of z_1, z_2a n d z_3dot

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

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

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

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 A(z_1),B(z_2) and C(z_3) be the three points in Argands plane The point A B and C are collinear if

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