FOR ANY TWO COMPLEX NUMBERS m AND n PROVE THAT arg( mn ) = arg(m)+arg(n)

Take the complex numbers as z1 and z2 .

We have z₁z₂=r₁e^iq1. r₂e^iq2

=r₁r₂^ei(q1+q2)

=(r₁r₂)(cos(q₁+q₂)+isin(q₁+q₂))

Arg(z₁z₂)= q₁+q₂=argz₁+argz₂

Hence Proved.