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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.


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