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Calculation rules for complex numbers
Operations with complex numbers must be performed according to special calculation rules.
Explanation
In the complex plane there are rules that must be followed in calculations. These rules are described in Lie groups. You may not switch to real numbers just like that. This is a kind of rule of thumb.
Example 1
In the complex plane, the calculation
gives a negative number as the result. It is therefore not
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You may not make a mapping to the real numbers until the last step. You can check this with a binomial development, because the root of the imaginary unit is
so that
Of course, we find the same answer.
Example 2
In a calculation, you may not suddenly introduce complex numbers and replace them later
In the complex plane you may also calculate differently
The simplest correct solution remains