### Root of a negative number

To calculate the **root of a negative number**, it must be reduced to an arithmetic root, with

##### Example 1

Negative numbers can be converted with the imaginary unit. Then you no longer have a minus sign. With a division you get

where *a* and *b* are positive numbers.

##### Example 2

The calculation

is wrong, although the outcome here happens to be correct. The property

applies only to arithmetic roots. Algebraic roots must first be reduced to arithmetic roots.

##### Example 3

The division

gives a positive number, but you probably wouldn't have expected anything else.