This product does have terms that add to 0, but the result is not a real number. The factors would need to be conjugates to result in a real product such as 97. Using FOIL shows that this is not the number 97.

$\displaystyle{\left({4}+{9}{i}\right)}{\left({9}+{4}{i}\right)}={4}{\left({9}\right)}+{4}{\left({4}{i}\right)}+{\left({9}{i}\right)}{\left({9}\right)}+{\left({9}{i}\right)}{\left({4}{i}\right)}={36}+{16}{i}+{81}{i}+{36}{{i}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle={36}+{97}{i}+{36}{\left(-{1}\right)}={36}+{97}{i}-{36}={97}{i}\usepackage{cmbright}\Huge\$