If `((3-z_1)/(2-z_1))((2-z_2)/(3-z_2))=k(k >0)` , then prove that points `A(z_1),B(z_2),C(3),a n dD(2)` (taken in clockwise sense) are concyclic.

If ((3-z_(1))/(2-z_(1)))((2-z_(2))/(3-z_(2)))=k(k>0), then prove that points A(z_(1)),B(z_(2)),C(3), and D(2) (taken in clockwise sense) are concyclic.

If arg[z_(3)-z_(2))]=arg[z_(3)(z_(2)-z_(1))], then find prove that O,z_(1),z_(2),z_(3) are concyclic, where O is the origin.

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

If a r g["z"_1("z"_3-"z"_2)]=a r g["z"_3("z"_2-"z"_1)] , then prove that O ,z_1, z_2, z_3 are concyclic, where O is the origin.

, a point 'z' is equidistant from three distinct points z_(1),z_(2) and z_(3) in the Argand plane. If z,z_(1) and z_(2) are collinear, then arg (z(z_(3)-z_(1))/(z_(3)-z_(2))). Will be (z_(1),z_(2),z_(3)) are in anticlockwise sense).

If z_(1),z_(2),z_(3),z_(4) are the affixes of four point in the Argand plane,z is the affix of a point such that |z-z_(1)|=|z-z_(2)|=|z-z_(3)|=|z-z_(4)| ,then prove that z_(1),z_(2),z_(3),z_(4) are concyclic.

Show that if z_(1)z_(2)+z_(3)z_(4)=0 and z_(1)+z_(2)=0 ,then the complex numbers z_(1),z_(2),z_(3),z_(4) are concyclic.