If `|z_(1)|=|z_(2)|=...=|z_(n)|=1`, then `|z_(1)+z_(2)+...+z_(n)| ` is equal to :

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

If z_(1),z_(2),z_(3) are the vertices of an equilational triangle ABC such that |z_(1)-i|=|z_(2)- i| = |z_(3)-i|, then |z_(1)+z_(2)+z_(3)| equals to

if z_(1),z_(2),z_(3),…..z_(n) are complex numbers such that |z_(1)|=|z_(2)| =….=|z_(n)| = |1/z_(1) +1/z_(2) + 1/z_(3) +….+1/z_(n)| =1 Then show that |z_(1) +z_(2) +z_(3) +……+z_(n)|=1

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)

Let z_(1) and z_(2) be two given complex numbers such that z_(1)/z_(2) + z_(2)/z_(1)=1 and |z_(1)| =3 , " then " |z_(1)-z_(2)|^(2) is equal to

If |z_(1)|=|z_(2)|, "is it necesssary that "z_(1) = z_(2) .

If z_(1),z_(2),……………,z_(n) lie on the circle |z|=R , then |z_(1)+z_(2)+…………….+z_(n)|-R^(2)|1/z_(1)+1/z_(2)+…….+1/z-(n)| is equal to

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

If |z_(1)+z_(2)|^(2) = |z_(1)|^(2) +|z_(2)|^(2) " the " 6/pi amp (z_(1)/z_(2)) is equal to ……