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Root of a negative number

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



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.


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