If `A (z_1), B (z_2) and C (z_3)` are three points in the argand plane where `|z_1 +z_2|=||z_1-z_2| and |(1-i)z_1+iz_3|=|z_1|+|z_3|-z_1|`, where `i = sqrt-1` then

If z_1, z_2, z_3 are three collinear points in |argand plane, then |(z_1,bar z_1,1),(z_2,barz_2,1),(z_3,barz_3,1)|=

If z_1,z_2,z_3 are three collinear points in argand plane, then |[z_1,barz_1,1],[z_2,barz_2,1],[z_3,barz_3,1]|

Let A(z_1),B(z_2) and C(z_3) be the vertices of an equilateral triangle in the Argand plane such that |z_1|=|z_2|=|z_3|. Then (A) (z_2+z_3)/(2z_1-z_2-z_3) is purely real (B) (z_2-z_3)/(2z_1-z_2-z_3) is purely imaginary (C) |arg(z_1/z_2)|=2 arg((z_3-z_2)/(z_1-z_2))| (D) none of these

The points A(z_1), B(z_2) and C(z_3) form an isosceles triangle in the Argand plane right angled at B, then (z_1-z_2)/(z_3-z_2) can be (A) 1 (B) -1 (C) -i (D) none of these

The points A(z_1), B(z_2) and C(z_3) form an isosceles triangle in the Argand plane right angled at B, then (z_1-z_2)/(z_3-z_2) can be (A) 1 (B) -1 (C) -i (D) none of these

On the Argand plane ,let z_(1) = - 2+ 3z,z_(2)= - 2-3z and |z| = 1 . Then

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.

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i| = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals:

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i| = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals: