### Root of a negative number

The **root of a negative number** must be reduced to an arithmetic root in order to calculate it, with

##### Explanation

Negative numbers can be converted with the imaginary unit. You then eliminate the minus sign. In a multiplication you get

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

##### Example 1

The result of the calculation

gives a negative number, what you probably did not expect. So it is not

##### Example 2

The calculation

is wrong. The property

is only valid for arithmetic roots. Algebraic roots must first be reduced to arithmetic roots.

##### Example 2

You can see that √−2 has no real value.