Suppose z1, z2 are two distinct complex numbers and a,b are real numbers.Statement-1: If z1+z2=a, z1z2=b, then arg(z1z2)=0Statement-2:  If z1+z2=a, z1z2=b, then z1¯=z2

Statement-2 is false. This can be seen by taking z1 and z2 to be distinct real numbers.For statement-1, take z1=α1+iβ1, z2=α2+iβ2. We have     β1+β2=0,α1β2+α2β1=0If β2=0, then β1=0, and statement-1 is true.If β2≠0, then β1=-β2 and α1-α2β2=0⇒   α1−α2=0 or α1=α2Thus, α2+iβ2= α1−iβ1  ⇒ z2=z1¯In this case also arg⁡z1z2=arg⁡z1z¯1=arg⁡z12=0