# What is the conjugate of 7+2i?

Mar 2, 2016

7 - 2i

#### Explanation:

If $a + \textcolor{b l u e}{\text{ bi " " is a complex number }}$

then $a - \textcolor{red}{\text{bi " " is the conjugate}}$

note that when you multiply a complex number by it's conjugate .

$\left(a + b i\right) \left(a - b i\right) = {a}^{2} + a b i - a b i + b {i}^{2} = {a}^{2} - {b}^{2}$

the result is a real number. This is a useful result.

[ i^2 = (sqrt-1)^2 = -1 ]

so 4-5i has conjugate 4 + 5i.

The real term remains unchanged but the imaginary term is the negative of what it was.