# How do you simplify (2+7i)(2-7i)?

Feb 6, 2016

53

#### Explanation:

distribute the brackets using FOIL

$\left(2 + 7 i\right) \left(2 - 7 i\right) = 4 - 14 i + 14 i - 49 {i}^{2}$

[ remember that ${i}^{2} = {\left(\sqrt{-} 1\right)}^{2} = - 1$]

so $4 - 14 i + 14 i - 49 {i}^{2} = 4 - 14 i + 14 i + 49$

= 53

(Worth noting here that when you multiply a complex number by it's conjugate you obtain a real number.)

ie. If a + bi is a complex number then a - bi is it's conjugate.

and (a+ bi)(a-bi) $= {a}^{2} + {b}^{2} \textcolor{b l a c k}{\text{ a real number}}$