### Complex number

With **complex numbers** you can perform calculations that are not possible with the usual numbers.

##### Explanation

When you learn to calculate, you start with the positive numbers 1, 2, 3 etc. Only later do you learn that you can also calculate with negative numbers. Then it all becomes a bit more abstract. Because what should you think about the task:

If there are two people in a waiting room at the doctor's, and five people go out, how many have to come in again to clear the waiting room?

You will say that this is not possible at all. That's right, but you can calculate it. *Do negative numbers actually exist?* If you're a bit older, you've also learned to calculate with fractions. Most people prefer to write digits after the decimal point instead of a fraction, as in the case of

because that's easier on your calculator. Fractions are called rational numbers. *Do you still need fractions?* Sometimes you have to work with roots. You use them if you want to calculate the oblique side of a triangle. Then you write something like

which is an irrational number. You cannot write that as a fraction of two integers. *And so you can continue for a while.* Then there are calculations that cannot be done at all. An example is

Should you then say that it is not possible, or is there a trick to continue calculating? Now, you use complex numbers for that.

## HistoryThe Italian mathematician Rafael Bombelli published the book |