How do you simplify 5/(1+2i)?

Apr 1, 2016

I found: $1 - 2 i$
I would multiply and divide by the complex conjugate of the denominator, i.e., $1 - 2 i$ to get:
$\frac{5}{1 + 2 i} \cdot \frac{1 - 2 i}{1 - 2 i} = \frac{5 - 10 i}{1 \cancel{- 2 i} \cancel{+ 2 i} - 4 {i}^{2}} =$
remembering that ${i}^{2} = - 1$
$= \frac{5 - 10 i}{1 + 4} = \frac{5 - 10 i}{5} = \frac{5}{5} - \frac{10}{5} i = 1 - 2 i$