Solution:
Given:
[tex](3-2i)(1+7i)[/tex]To find the product, we multiply the terms in the second parentheses by each term in the first parentheses.
Thus, we have
[tex]\begin{gathered} 3(1+7i)-2i(1+7i) \\ open\text{ parentheses,} \\ 3+21i-2i-14i^2 \\ but\text{ i}^2=-1 \\ thus,\text{ we have} \\ 3+21i-2i-14(-1) \\ collect\text{ like terms,} \\ (3+14)+i(21-2) \\ \Rightarrow17+19i \end{gathered}[/tex]Hence, the product of the complex numbers is
[tex]17+19i[/tex]The correct option is B