If `z_1=a + ib and z_2 = c + id` are complex numbers such that `|z_1|=|z_2|=1 and Re(z_1 bar z_2)=0` , then the pair ofcomplex nunmbers `omega_1=a+ic and omega_2=b+id` satisfies

If z_(1) = a + ib " and " z_(2) + c id are complex numbers such that |z_(1)| = |z_(2)| = 1 and Re (z_(1)bar (z)_(2)) = 0 , then the pair of complex numbers w_(1) = a + ic " and " w_(2) = b id satisfies :

If z 1 ​ =a+ib and z 2 ​ =c+id are complex numbers such that ∣z 1 ​ ∣=∣z 2 ​ ∣=1 and Re(z 1 ​ z 2 ​ ​ )=0, then the pair of complex numbers w 1 ​ =a+ic and w 2 ​ =b+id satisfy

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 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))/(z_(1)+z_(2))|=1 , then

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)|= |z_(2)| , then is it necessary that z_(1) = z_(2)

If a complex number z satisfies |z| = 1 and arg(z-1) = (2pi)/(3) , then ( omega is complex imaginary number)

If z, z _1 and z_2 are complex numbers such that z = z _1 z_2 and |barz_2 - z_1| le 1 , then maximum value of |z| - Re(z) is _____.

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