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_n)` be the orthocenrter of triangle `A B C` , then find `z_ndot`

A(z_1) , B(z_2) and C(z_3) are the vertices of triangle ABC inscribed in the circle |z|=2,internal angle bisector of angle A meets the circumcircle again at D(z_4) .Point D is:

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 dC_1(z_3) , obtain the complex numbers associated with the vertices A ,B ,C in terms of z_1, z_2a n dz_3dot

lf z_1,z_2,z_3 are vertices of an equilateral triangle inscribed in the circle |z| = 2 and if z_1 = 1 + iotasqrt3 , then

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 he 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

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 he orthocentre of the triangle, then prove that z_1( z )_2+( z )_1z_2=_2( z )_3+( z )_2z_3=z_3( z )_1+( z )_(3)z_1dot

If A(z_(1)),B(z_(2)), C(z_(3)) are the vertices of an equilateral triangle ABC, then arg (2z_(1)-z_(2)-z_(3))/(z_(3)_z_(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 the points A(z),B(-z),a n dC(1-z) are the vertices of an equilateral triangle A B C , then (a)sum of possible z is 1/2 (b)sum of possible z is 1 (c)product of possible z is 1/4 (d)product of possible z is 1/2

z_1a n dz_2 are the roots of 3z^2+3z+b=0. if O(0),(z_1),(z_2) form an equilateral triangle, then find the value of bdot

z_1a n dz_2 are the roots of 3z^2+3z+b=0. if O(0),(z_1),(z_2) form an equilateral triangle, then find the value of bdot