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)and z_(3) are the vertices of an equilateral 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.

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

If z_(1), z_(2), z_(3) are three complex numbers in A.P., then they lie on

If z_(1),z_(2),z_(3) represent the vertices of an equilateral triangle such that |z_(1)|=|z_(2)|=|z_(3)| , then

The complex numbers z_(1), z_(2), z_(3) are three vertices of a parallelogram taken in order then the fourth vertex is

If |z_(1)|=|z_(2)| and arg z_(1) + arg z_(2)=0 then

The points z_(1),z_(2),z_(3),z_(4) in complex plane are the vertices of a parallelogram, taken in order if :

If |z_(1)+z_(2)|=|z_(1)-z_(2)| , then the difference of the arguments of z_(1) and z_(2) is

Complex numbers z_(1),z_(2)andz_(3) are the vertices A,B,C respectivelt 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)).

Let z_(1) and z_(2) be n^(th ) roots of unity which subtend a right angle at the origin. Then n must be of the form.