You may have seen the plus and minus signs and thought they would make the product real. 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)}={\left({4}\right)}{\left({9}\right)}+{\left({4}\right)}{\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}-{65}{i}-{36}{\left(-{1}\right)}={36}-{65}{i}+{36}={72}-{65}{i}\usepackage{cmbright}\Huge\$