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 Im(z_(1)+z_(2))=0, Im(z_(1)z_(2))=0 then

If z_(1), z_(2) are two complex numbers such that Im(z_(1)+z_(2))=0 and Im(z_(1) z_(2))=0 , 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)-z_(2))/(z_(1)+z_(2))|=1 , 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)-z_(2))/(z_(1)+z_(2))|=1 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| show that Im (z_1/z_2)=0