# How do you find the product of the complex number: (5-2i)(5+2i)?

Feb 13, 2016

29

#### Explanation:

distribute the brackets using FOIL( or any method you use)

$\left(5 - 2 i\right) \left(5 + 2 i\right) = 25 + 10 i - 10 i - 4 {i}^{2}$

[ this process is useful in complex numbers as the product produces a real number - the 2nd bracket is the complex conjugate of the 1st and vice-versa.]

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

$\Rightarrow \left(5 - 2 i\right) \left(5 + 2 i\right) = 25 + 10 i - 10 i + 4 = 29 \textcolor{b l a c k}{\text{ a real number}}$