# What is the complex conjugate of 3i+4?

Apr 22, 2015

If $z = 4 + 3 i$ then $\overline{z} = 4 - 3 i$

A conjugate of a complex number is a number with the same real part and an oposite imaginary part.

In the example :
$r e \left(z\right) = 4$ and $i m \left(z\right) = 3 i$
So the conjugate has:
$r e \left(\overline{z}\right) = 4$ and $i m \left(\overline{z}\right) = - 3 i$
So $\overline{z} = 4 - 3 i$

Note to a question : It is more usual to start a complex number with the real part so it would rather be written as $4 + 3 i$ not as $3 i + 4$

Dec 8, 2015

$4 - 3 i$

#### Explanation:

To find a complex conjugate, simply change the sign of the imaginary part (the part with the $i$). This means that it either goes from positive to negative or from negative to positive.

As a general rule, the complex conjugate of $a + b i$ is $a - b i$.

Notice that $3 i + 4 = 4 + 3 i$, which is the generally accepted order for writing terms in a complex number.

Therefore, the complex conjugate of $4 + 3 i$ is $4 - 3 i$.