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) are the vertices of an isoscles triangle right angled at z_(2) , then

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 =

If z_(1),z_(2)andz_(3) are the vertices of an equilasteral triangle with z_(0) as its circumcentre , then changing origin to z^(0) ,show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0, where z_(1),z_(2),z_(3), are new complex numbers of the vertices.

Let the complex numbers z_(1),z_(2) and z_(3) be the vertices of an equailateral triangle. If z_(0) is the circumcentre of the triangle , then prove that z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3z_(0)^(2) .

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

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

If the points z_(1),z_(2),z_(3) are the vertices of an equilateral triangle in the Argand plane, then which one of the following is not correct?

If z_(1),z_(2),z_(3) be vertices of an equilateral triangle occurig in the anticlockwise sense, then

z_(1),z_(2),z_(3) are the vertices of an equilateral triangle taken in counter clockwise direction. If its circumference is at the origin and z_(1)=1+i , then