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Negative square

To perform calculations with complex numbers, the definition of the imaginary unit is sufficient

i ² = –1

It enables a square to be negative.

 

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Explanation

It still has other consequences, as there is

and that's positive again. There is also a 4th power that gives a negative result. To this end, we first square a complex number and obtain

so applies

 

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Example 1

For the root of the imaginary unit applies

 

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