The complex numbers `z_1,=1+2i,z_2=4-2i and z_3=1-6i` form the vertices of a (A) a right angled triangle (B) isosceles triangle (C) equilateral triangle (D) triangle whose one of the sides is of length 8

The complex numbers z_1, z_2 and z_3 satisfying (z_1-z_3)/(z_2- z_3)= (1-i sqrt3)/2 are the vertices of triangle, which is :

The complex numbers z_1, z_2 and z_3 satisfying (z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2 are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

The complex numbers z_1 z_2 and z3 satisfying (z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2 are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

If z=1+3i then show that z , iz and z+zi form a right angled isosceles triangle.

If the complex numbers z_(1) , z_(2) , z_(3) represents the vertices of an equilateral triangle such that |z_1| = |z_2| = |z_3| then

Complex numbers z_1 , z_2 , z_3 are the vertices A, B, C respectively of an isosceles right angled triangle with right angle at C and (z_1- z_2)^2 = k(z_1 - z_3) (z_3 -z_2) , then find k.

Complex numbers z_1 , z_2, z_3 are the vertices A, B, C respectively of an isosceles right angled triangle with right angle at C. Show that (z_1-z_2)^2 =2 (z_1 - z_3) (z_3-z_2) .