The two factors are complex conjugates, so their product will result in a real number. Use FOIL.

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

$\displaystyle={16}-{\left({81}\right)}{\left(-{1}\right)}={16}+{81}={97}\usepackage{cmbright}\Huge\$