Solution
= Solution
With $z_1=a+ib$ and $z_2=c+id$, direct multiplication gives $z_1z_2=(ac-bd)+i(ad+bc)$. Taking the <complex conjugate> yields
$$
(z_1z_2)^*=(ac-bd)-i(ad+bc)=(a-ib)(c-id)=\boxed{z_1^*z_2^*.}
$$
= Solution
With $z_1=a+ib$ and $z_2=c+id$, direct multiplication gives $z_1z_2=(ac-bd)+i(ad+bc)$. Taking the <complex conjugate> yields
$$
(z_1z_2)^*=(ac-bd)-i(ad+bc)=(a-ib)(c-id)=\boxed{z_1^*z_2^*.}
$$