If `z_1 and z_2` are two complex numbers such that `|z_1|lt1lt|z_2|` then prove that `|(1-z_1barz_2)/(z_1-z_2)|lt1`

If z_(1) and z_(2) are two complex numbers such that |z_(1)| lt 1 lt |z_(2)| , then prove that |(1- z_(1)barz_(2))//(z_(1)-z_(2))| lt 1

If z_1 and z_2 are two complex numbers such that |\z_1|=|\z_2|+|z_1-z_2| show that Im (z_1/z_2)=0

If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)| , then is it necessary that z_(1) = z_(2)

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

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

Let z_1, z_2 be two complex numbers with |z_1| = |z_2| . Prove that ((z_1 + z_2)^2)/(z_1 z_2) is real.

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If z_1 and z_2 are two complex numbers such that |(barz_1-2barz_2)(2-z_1barz_2)|=1 then (A) |z_1|=1, if |z_2|!=1 (B) |z_1|=2, if |z_2|!=1 (C) |z_2|=2, if |z_1|!=1 (D) |z_2|=1, if |z_1|!=2

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( z )_2dot