Let `z_1, z_2........ z_n` be equi-modular non-zero complex numbers such that `z_1+z_2+z_3+...+z_n=0` Then `Re(sum_(j=1)^n sum_(k=1)^n(z_j/z_k))`

Let z_1,z_2, z_3,......, z_n be complex numbers such that |z_1|=|z_2|=...=|z_n|=1. If z=(sum_(k=1)^n z_k)(sum_(k=1)^n1/(z_k)) then prove that z is a real number

Let z_(1)z_(2),z_(3)...z_(n) be the complex numbers such that |z_(1)|=|z_(2)|...|z_(n)|=1. If z=(sum_(k=1)^(n)z_(k))(sum_(k=1)^(n)(1)/(z_(k))) then proves that z is a real number 0

Let z_1,z_2, z_3, z_n be the complex numbers such that |z_1|=|z_2|=|z_n|=1. If z=(sum_(k=1)^n z_k)(sum_(k=1)^n1/(z_k)) then proves that z is a real number

Let z_1z_2, z_3 z_n be the complex numbers such that |z_1|=|z_2||z_n|=1. If z=(sum_(k=1)^n z_k)(sum_(k=1)^n1/(z_k)) then proves that z is a real number

Let z_(1),z_(2),z_(3),……z_(n) be the complex numbers such that |z_(1)|= |z_(2)| = …..=|z_(n)| = 1 . If z = (sum_(k=1)^(n)z_(k)) (sum_(k=1)^(n)(1)/(z_(k))) then prove that : z is a real number .

Let z_(1),z_(2),z_(3),...,z_(n) be non zero complex numbers with |z_(1)|=|z_(2)|=|z_(3)|...=|z_(n)| then the number z=((z_(1)+z_(2))(z_(2)+z_(3))(z_(3)+z_(4))...(z_(n-1)+z_(n))(z_(n)+z_(1)))/(z_(1)z_(2)z_(3)...z_(n)) is

Let z_1 and z_2 be two non - zero complex numbers such that z_1/z_2+z_2/z_1=1 then the origin and points represented by z_1 and z_2

Let Z_1 and Z_2 are two non-zero complex number such that |Z_1+Z_2|=|Z_1|=|Z_2| , then Z_1/Z_2 may be :

Let Z_1 and Z_2 are two non-zero complex number such that |Z_1+Z_2|=|Z_1|=|Z_2| , then Z_1/Z_2 may be :