# How do I find the complex conjugate of 10+6i?

Mar 23, 2018

$10 - 6 i$

#### Explanation:

$\text{Given a complex number "z=a+-bi" then}$

"the "color(blue)"complex conjugate "=acolor(red)(∓)bi

$\text{note that the product of a complex number and it's}$
$\text{conjugate results in a real number}$

$\left(a + b i\right) \left(a \textcolor{red}{-} b i\right) = {a}^{2} + {b}^{2} \leftarrow \textcolor{b l u e}{\text{real number}}$

$\text{the conjugate of "10+6i" is } 10 \textcolor{red}{-} 6 i$

$\text{and "(10+6i)(10-6i)=100+36=136larrcolor(red)"real}$