# Conjugate complex numbers

Calculator and formula for conjugating complex numbers

## Conjugate calculator

Conjugate a complex number

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## Conjugate a complex number

Every complex number has a so-called complex conjugate number. These conjugate complex numbers are needed in the division, but also in other functions.

As an example we take the number $$5+3i$$ . The complex number conjugated to $$5+3i$$ is $$5-3i$$. The real parts of the two numbers are the same, the imaginary parts of the two differ only by the sign.

Let's take a look at the product of the two numbers

$$(5+3i)·(5-3i) = 25-15i + 15i-9i = 25+9 = 34$$

The product of the complex numbers and their conjugates is real. This is a special property of conjugate complex numbers that will prove useful.

For the conjugate complex number   $$a-bi$$   schreibt man   $$\overline{z}=a-bi$$.

So in the example above  $$\overline{5+3i}=5-3i$$

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