Use the distributive property of multiplication and simplify, remembering that $\displaystyle{{i}}^{{2}}=-{1}\usepackage{cmbright}\Huge\$ .

$\displaystyle{\left({2}+{i}\right)}{\left({7}-{3}{i}\right)}={\left({2}\right)}{\left({7}-{3}{i}\right)}+{\left({i}\right)}{\left({7}-{3}{i}\right)}\usepackage{cmbright}\Huge\$

$\displaystyle={\left({2}\right)}{\left({7}\right)}+{\left({2}\right)}{\left(-{3}{i}\right)}+{\left({i}\right)}{\left({7}\right)}+{\left({i}\right)}{\left(-{3}{i}\right)}\usepackage{cmbright}\Huge\$

$\displaystyle={14}-{6}{i}+{7}{i}-{3}{{i}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle={14}-{6}{i}+{7}{i}+{3}\usepackage{cmbright}\Huge\$

$\displaystyle={17}+{i}\usepackage{cmbright}\Huge\$