If ` z_1 and z_2 ` are two compled 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)| then

Statement-1 If|z_1| and |z_2| are two complex numbers such that |z_1|=|z_2|+|z_1-z_2|, then Im(z_1/z_2)=0 and Statement-2: arg(z)=0 =>z is purely 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) and z_(2) are two complex numbers such that z_(1)+2,1-z_(2),1-z, then

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 nonzero complex numbers such that |z_1-z_2|=|z_1|-|z_2| then arg z_1 -arg z_2 is equal to