Let `z_(1),z_(2)` and `z_(3)` be complex numbers such that `|z_(1)|=|z_(2)|=|z_(3)|=1` then prove that `|z_(1)+z_(2)+z_(3)|=|z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)|`

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

Let z_(1), z_(2), z_(3) be three complex numbers such that |z_(1)| = |z_(2)| = |z_(3)| = 1 and z = (z_(1) + z_(2) + z_(3))((1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))) , then |z| cannot exceed

Let z_(1),z_(2),z_(3) be complex numbers (not all real) such that |z_(1)|=|z_(2)|=|z_(3)|=1 and 2(z_(1)+z_(2)+z_(3))-3z_(1)z_(2)z_(3) is real.Then,Max(arg(z_(1)),arg(z_(2)),arg(z_(3))) (Given that argument of z_(1),z_(2),z_(3) is possitive ) has minimum value as (k pi)/(6) where (k+2) is

Given the z_(1),z_(2) and z_(3) are complex numbers with |z_(1)|=1,|z_(2)|=1,|z_(3)|=1, and z_(1)+z_(2)+z_(3)=1 and z_(1)z_(2)z_(3)=1 find |(z_(1)+2)(z_(2)+2)(z_(3)+2)|

If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)

If complex numbers z_(1)z_(2) and z_(3) are such that |z_(1)| = |z_(2)| = |z_(3)| , then prove that arg((z_(2))/(z_(1)) = arg ((z_(2) - z_(3))/(z_(1) - z_(3)))^(2)

If z_(1),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 then |z_(1)+z_(2)+z_(3)| is equal to