# How do you simplify (5 + 2i)(5 - 2i) and write in a+bi form?

May 17, 2016

$29$

#### Explanation:

Given,

$\left(\textcolor{red}{5} \textcolor{w h i t e}{i} \textcolor{b l u e}{+ 2 i}\right) \left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{5} \textcolor{w h i t e}{i} \textcolor{t e a l}{- 2 i}\right)$

Use the F.O.I.L. (first, outside, inside, last) method to expand the brackets.

$= \textcolor{red}{5} \left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{5}\right) \textcolor{w h i t e}{i} \textcolor{red}{+ 5} \left(\textcolor{t e a l}{- 2 i}\right) \textcolor{w h i t e}{i} \textcolor{b l u e}{+ 2 i} \left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{5}\right) \textcolor{w h i t e}{i} \textcolor{b l u e}{+ 2 i} \left(\textcolor{t e a l}{- 2 i}\right)$

Simplify.

$= 25 - 10 i + 10 i - 4 {i}^{2}$

$= 25 - 4 {i}^{2}$

Since ${i}^{2} = - 1$, the expression simplifies to,

$= 25 - 4 \left(- 1\right)$

$= 25 + 4$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{29} \textcolor{w h i t e}{\frac{a}{a}} |}}}$