You may have simplified by dividing 10 by 1 and by i, obtaining $\displaystyle\frac{{10}}{{1}}+\frac{{10}}{{i}}\usepackage{cmbright}\Huge\$ and then rationalizing $\displaystyle\frac{{10}}{{i}}\usepackage{cmbright}\Huge\$ to get $\displaystyle-{10}{i}\usepackage{cmbright}\Huge\$ .

Treat the division as a fraction and rationalize the denominator: $\displaystyle\frac{{10}}{{{1}+{i}}}=\frac{{10}}{{{1}+{i}}}\cdot\frac{{{1}-{i}}}{{{1}-{i}}}\usepackage{cmbright}\Huge\$

The correct answer is $\displaystyle{5}-{5}{i}\usepackage{cmbright}\Huge\$ .