If `|z-1|<=2` and `|omega z-1-omega^2|=a` then (a) `0<=a<=2` (b) `1/2<=a<=sqrt(3)/2` (c) `sqrt(3)/2-1/2<=a<=1/2+sqrt(3)/2`

If |z_(1)|=|z_(2)|=......=|z_(n)|=1, prove that |z_(1)+z_(2)+z_(3)++z_(n)|=(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))++(1)/(z_(n))

If |z_(1)|=|z_(2)|=....|z_(n)|=1 , then show that, |z_(1)+z_(2)+z_(3)+....z_(n)|= |(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))+...+(1)/(z_(n))|

If |z_(1)|=|z_(2)|=...............=|z_(n)|=1 then |(1)/(z_(1))+(1)/(z_(2))+.........+(1)/(z_(n))|

If |z_(1)| = |z_(2)| = 1, z_(1)z_(2) ne -1 and z = (z_(1) + z_(2))/(1+z_(1)z_(2)) then

If |z_(1)|!=1,|(z_(1)-z_(2))/(1-bar(z)_(1)z_(2))|=1, then

If |z_(1)| = |z_(2)| = ….. |z_(n)| = 1 , prove that |z_(1) + z_(2) + …….. z_(n)| = |(1)/(z_(1)) + (1)/(z_(2)) + ……….. + (1)/(z_(n))| .

If |z_(1)|= |z_(2)|= ….= |z_(n)|=1 , prove that |z_(1) + z_(2) + …+ z_(n)|= |(1)/(z_(1)) + (1)/(z_(2)) + …(1)/(z_(n))|

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

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

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then z 1 ​ +z 2 ​ is equal to