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.