If `z_1 , z_2 and z_3` ( in anticlockwise sense) represents the vertices of a triangle, find the centroid, incentre, circumstance and the orthocentre of the triangle.

If z_(1), z_(2),z_(3) represent the vertices of a triangle, then the centroid of the triangle is given by

In a triangle, if orthocentre, circumcentre, incentre and centroid coincide, then the triangle must be

If the complex numbers iz,z and z+iz represent the three vertices of a triangle,then the area of the triangle is

If z_(1),z_(2),z_(3),z_(4), represent the vertices of a rhombus taken in anticlockwise order,then

On the Argand plane z_(1),z_(2) and z_(3) are respectively,the vertices of an isosceles triangle ABC with AC=BC and equal angles are theta. If z_(4) is the incenter of the triangle,then prove that (z_(2)-z_(1))(z_(3)-z_(1))=(1+sec theta)(z_(4)-z_(1))^(2)