Let `z` be not a real number such that `(1+z+z^2)//(1-z+z^2) in R ,` then prove tha `|z|=1.`

Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then prove that |z|=1.

If z_(1) and z_(2) are two complex number such that |z_(1)|<1<|z_(2)| then prove that |(1-z_(1)bar(z)_(2))/(z_(1)-z_(2))|<1

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 and z_2 be two complex numbers such that z_1+z_2 and z_1z_2 both are real, theb

Let z_(1),z_(2) be two complex numbers such that z_(1)+z_(2) and z_(1)z_(2) both are real, then

Let z_(1),z_(2) be two complex numbers such that z_(1)+z_(2) and z_(1)z_(2) both are real, then

z_1,z_2,z_3 are complex number and p,q,r are real numbers such that: p/(|z_2-z_3|)= q/(|z_3-z_1|)= r/(|z_1-z_2|) . Prove that p^2/(z_2-z_3)= q^2/(z_3-z_1)= r^2/(z_1-z_2)=0

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

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