Basic complex number identities involving modulus and argument

Prove: |zw|=|z||w| (modulus of product equals product of moduli)
Prove: arg(zw)=arg(z)+arg(w) (argument of product equals sum of arguments)
Prove: zz*=|z|^2 (complex number multiplied by its own conjugate equals modulus squared)

Recorded during a lesson so there are some pauses.