If `|z| <= 1 and |omega| <= 1,` show that `|z-omega|^2 <= (|z|-|omega|)^2+(arg z-arg omega)^2`

If |z-(4)/(z)|=2 then the maximum value of |z| is

Find the maximum and minimum values of |z| satisfying |z+(1)/(z)|=2

The maximum value of |z| when z satisfies the condition |z+(2)/(z)|=2 is

If |z+(4)/(z)|=2, find the maximum and minimum values of |z|.

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+bar(z)|+|z-bar(z)|=8 then z lies on

If |z_(1)|=|z_(2)|=|z_(3)|=|z_(4)| , then the points representing z_(1),z_(2),z_(3),z_(4) are :

If z_(1) and z_(2) are complex number and (z_(1))/(z_(2)) is purely imaginary then |((z1+z2)/(z1-z2))|=

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find z_(1)+z_(2) .

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