Find the circumstance of the triangle whose vertices are given by the complex numbers `z_(1),z_(2)` and `z_(3)`.

Find the circumcentre of the triangle whose vertices are given by the complex numbers z_(1),z_(2) and z_(3) .

In the complex plane, the vertices of an equlitateral triangle are represented by the complex numbers z_(1),z_(2) and z_(3) prove that, (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

18.In the complex plane,the vertices of an equilateral triangle are represented by the complex numbers z_(1),z_(2) and z_(3) prove that (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

If two triangles whose vertices are respectively the complex numbers z_(1),z_(2),z_(3) and a_(1),a_(2),a_(3) are similar, then the determinant. |{:(z_(1),a_(1),1),(z_(2),a_(2),1),(z_(3),a_(3),1):}| is equal to

If two triangles whose vertices are respectively the complex numbers z_(1),z_(2),z_(3) and a_(1),a_(2),a_(3) are similar, then the determinant. |{:(z_(1),a_(1),1),(z_(2),a_(2),1),(z_(3),a_(3),1):}| is equal to

Le z_(1) and z_(2) be non-zero complex numbers satisfying the equation,z_(1)^(2)-2z_(1)z_(2)+2z_(2)^(2)=0. The geometrical nature of the triangle whose vertices are the origin and the points representing z_(1), and z_(2) is

The vertices A,B,C of an isosceles right angled triangle with right angle at C are represented by the complex numbers z_(1) z_(2) and z_(3) respectively. Show that (z_(1)-z_(2))^(2)=2(z_(1)-z_(3))(z_(3)-z_(2)) .

If the vertices of an equilateral triangle be represented by the complex numbers z_(1),z_(2),z_(3) on the Argand diagram, then prove that, z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).

The three vertices of a triangle are represented by the complex numbers 0 , z_(1) and z_(2) . If the triangle is equilateral , then :