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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

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