You may have thought that multiplying a complex number by itself would result in a real number, but that only works if it is a purely imaginary number (real part equal to 0). Using FOIL shows that this is not the number 45.

$\displaystyle{\left({6}-{3}{i}\right)}{\left({6}-{3}{i}\right)}={\left({6}\right)}{\left({6}\right)}-{\left({6}\right)}{\left({3}{i}\right)}-{\left({3}{i}\right)}{\left({6}\right)}+{\left({3}{i}\right)}{\left({3}{i}\right)}={36}-{18}{i}-{18}{i}+{9}{{i}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle={36}-{36}{i}+{9}{\left(-{1}\right)}={27}-{36}{i}\usepackage{cmbright}\Huge\$