Conjugate complex numbers

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  \(\overline{5+3i}=5-3i\)