Given two complex tori $X_1$ and $X_2$, there is always a canonical isomorphism
$\widehat{X_1 \times X_2} \cong \widehat{X}_1 \times \widehat{X}_2$,
see Birkenhake-Lange's book Complex Abelian Varieties, Exercise 11 page 43.
Given two complex tori $X_1$ and $X_2$, there is always a canonical isomorphism
$\widehat{X_1 \times X_2} \cong \widehat{X}_1 \times \widehat{X}_2$,
see Birkenhake-Lange's book Complex Abelian Varieties, Exercise 11 page 43.