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 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 .

If z_1,z_2 are two complex numbers such that Im(z_1+z_2)=0,Im(z_1z_2)=0 , then:

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

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_1a n dz_2 be two complex numbers such that ( z )_1+i( z )_2=0 and arg(z_1z_2)=pidot Then, find a r g(z_1)dot

Let z_1, z_2, z_3 be the three nonzero complex numbers such that z_2!=1,a=|z_1|,b=|z_2|a n d c=|z_3|dot Let |a b c b c a c a b|=0 a r g(z_3)/(z_2)=a r g((z_3-z_1)/(z_2-z_1))^2 orthocentre of triangle formed by z_1, z_2, z_3, i sz_1+z_2+z_3 if triangle formed by z_1, z_2, z_3 is equilateral, then its area is (3sqrt(3))/2|z_1|^2 if triangle formed by z_1, z_2, z_3 is equilateral, then z_1+z_2+z_3=0

Let z_(1) and z_(2) be any two non-zero complex numbers such that 3|z_(1)|=2|z_(2)|. "If "z=(3z_(1))/(2z_(2)) + (2z_(2))/(3z_(1)) , then

Let z_1,z_2 be complex numbers with |z_1|=|z_2|=1 prove that |z_1+1| +|z_2+1| +|z_1 z_2+1| geq2 .