Write as a fraction. Rationalize the denominator by multiplying the numerator and denominator by the denominator's complex conjugate.

$\displaystyle\frac{{10}}{{{1}+{i}}}=\frac{{10}}{{{1}+{i}}}\cdot\frac{{{1}-{i}}}{{{1}-{i}}}=\frac{{{10}-{10}{i}}}{{{1}-{{i}}^{{2}}}}=\frac{{{10}-{10}{i}}}{{{1}-{\left(-{1}\right)}}}\usepackage{cmbright}\Huge\$

$\displaystyle=\frac{{{10}-{10}{i}}}{{2}}=\frac{{10}}{{2}}-\frac{{10}}{{2}}{i}={5}-{5}{i}\usepackage{cmbright}\Huge\$