Find the relation if `z_1, z_2, z_3, z_4` are the affixes of the vertices of a parallelogram taken in order.

The points, z_1,z_2,z_3,z_4, in the complex plane are the vertices of a parallelogram taken in order, if and only if (a) z_1+z_4=z_2+z_3 (b) z_1+z_3=z_2+z_4 (c) z_1+z_2=z_3+z_4 (d) None of these

If z_(1), z_(2), z_(3), z_(4) are complex numbers, show that they are vertices of a parallelogram In the Argand diagram if and only if z_(1) + z_(3)= z_(2) + z_(4)

If z_(1),z_(2)andz_(3) are the affixes of the vertices of a triangle having its circumcentre at the origin. If zis the affix of its orthocentre, prove that Z_(1)+Z_(2)+Z_(3)-Z=0.

If z_1, z_2, z_3 be the affixes of the vertices A, B and C of a triangle having centroid at G such ;that z = 0 is the mid point of AG then 4z_1 + z_2 + z_3 =

If z_1, z_2, z_3 be the affixes of the vertices A, B Mand C of a triangle having centroid at G such ;that z = 0 is the mid point of AG then 4z_1 + Z_2 + Z_3 =

The complex number z_(1),z_(2),z_(3) are the vertices A, B, C of a parallelogram ABCD, then the fourth vertex D is:

z_1, z_2, z_3,z_4 are distinct complex numbers representing the vertices of a quadrilateral A B C D taken in order. If z_1-z_4=z_2-z_3 and "arg"[(z_4-z_1)//(z_2-z_1)]=pi//2 , the quadrilateral is

If the complex number z_1,z_2 and z_3 represent the vertices of an equilateral triangle inscribed in the circle |z|=2 and z_1=1+isqrt(3) then (A) z_2=1,z_3=1-isqrt(3) (B) z_2=1-isqrt(3),z_3=-isqrt(3) (C) z_2=1-isqrt(3), z_3=-1+isqrt(3) (D) z_2=-2,z_3=1-isqrt(3)

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 z_1, z_2, z_3, z_4 are

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.