# How do you simplify (5+i)(8+i) and write the complex number in standard form?

Oct 13, 2016

$39 + 13 i$

#### Explanation:

$\textcolor{b l u e}{\left(5 + i\right)} \textcolor{b r o w n}{\left(8 + i\right)}$

Multiply everything in the RHS brackets by everything in the LHS brackets.

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color(blue)(
color(brown)(
$\left[\textcolor{b l u e}{5 \times} \textcolor{b r o w n}{8}\right] + \left[\textcolor{b l u e}{5 \times} \textcolor{b r o w n}{i}\right] \text{ "+" } \left[\textcolor{b l u e}{i \times} \textcolor{b r o w n}{8}\right] + \left[\textcolor{b l u e}{i \times} \textcolor{b r o w n}{i}\right]$

$40 + 5 i + 8 i + \left(- 1\right)$

$39 + 13 i$