`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:

If z_(1),z_(2),z_(3) are vertices of an equilateral triangle inscribed in the circle |z|=2 and if z_(1)=1+iota sqrt(3), then

Let the complex numbers z_1, z_2 and z_3 represent the vertices A, B and C of a triangle ABC respectively, which is inscribed in the circle of radius unity and centre at origin.The internal bisector of the angle A meets the circumcircle again at the point D, Which is represented by the complex number z_4 and altitude from A to BC meets the circumcircle at E. given by z_5. Then arg([z_2z_3]/z_4^2) is equal to

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then

If the points A(z),B(-z) and C(z+1) are vertices of an equilateral triangle then

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

The points A(x,y), B(y, z) and C(z,x) represents the vertices of a right angled triangle, if

In hat harr ABC,A(z_(1)),B(z_(2)), and C(z_(3)) are inscribed in the circle |z|=5. If H(z_(n)) be the orthocenrter of triangle ABC, then find z_(n) .

A, B, C are the points representing the complex numbers z_1, z_2, z_3 respectively on the complex plane and the circumcentre of the triangle ABC lies at the origin. If the altitude AD of the triangle ABC meets the circumcircle again at P, then P represents the complex number