" (v) "z+(1)/(z)=3,z!=0

The centre of a square ABCD is at z_(0). If A is z_(1) ,then the centroid of the ABC is 2z_(0)-(z_(1)-z_(0))(b)(z_(0)+i((z_(1)-z_(0))/(3))(z_(0)+iz_(1))/(3) (d) (2)/(3)(z_(1)-z_(0))

Show that if z_(1)z_(2)+z_(3)z_(4)=0 and z_(1)+z_(2)=0 ,then the complex numbers z_(1),z_(2),z_(3),z_(4) are concyclic.

Show that if z_(1)z_(2)+z_(3)z_(4)=0 and z_(1)+z_(2)=0 ,then the complex numbers 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; then (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

If the complex numbers z_(1), z_(2), z_(3) represent the vertices of an equilateral triangle, and |z_(1)|= |z_(2)| = |z_(3)| , prove that z_(1)+ z_(2) + z_(3)=0

a. Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=rgt0 and z_(1)+z_(2)+z_(3)!=0 . Prove that |(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1))/(z_(1)+z_(2)+z_(3))|=r b. Find all cube roots of sqrt(3)+i .

In the complex plane, the vertices of an equlitateral triangle are represented by the complex numbers z_(1),z_(2) and z_(3) prove that, (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

18.In the complex plane,the vertices of an equilateral triangle are represented by the complex numbers z_(1),z_(2) and z_(3) prove that (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

If 2z_(1)-3z_(2)+z_(3)=0, then z_(1),z_(2) and z_(3) are represented by