If `|z_1|=|z_2|=...................=|z_n|=1`, then `|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|=|z_3|=......=|z_n|=1 , then |z_1+z_2+z_3+......+z_n|=

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

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

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 abs(z_1) = abs(z_2) = ........= abs(z_n) =1, then show that abs(z_1+ z_2+.......+z_n) = abs(frac{1}{z_1}+frac{1}{z_2}+.........frac{1}{z_n})

If |z_1|=|z_2|=|z_3|"…."=|z_n|=1 then |z_(1)+z_(2)+"….."+z_(n)|=

If z_(1), z_(2),……..,z_(n) are complex numbers such that |z_(1)| = |z_(2)| = …….. = |z_(n)| = 1 , then |z_(1) + z_(2) +……..+ z_(n)| is equal to a) |z_(1)z_(2)z_(3)…..z_(n)| b) |z_(1)|+|z_(2)|+…….+|z_(n)| c) |(1)/(z_(1)) + (1)/(z_(2)) + ……….+ (1)/(z_(n))| d)n

If z_(1),z_(2).........z_(n)=z, then arg z_(1)+arg z_(2)+......+argz_(n) and arg z differ by a