Proof:
1) S=P+jQ = VI*
if P=V*I then,
2) S=V*I + jQ = VI*
3) V*I + jQ = P+jQ
4) From like term in 3), P=V*I.
Verify,
let V=v*exp(a), I = i*exp(b)
S=VI* = vi*exp(a-b) = P+jQ
S*=V*I = vi*exp[-(a-b)] = P-jQ
S+S* = 2P = 2vicos(a-b)
P=vi*cos(a-b) = vi * R{exp(a-b)] = Re[vexp(a)* iexp(-b)]...