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the usual operations of addition and multiplication, also form a field. The complex numbers consist of expressions
: with real,where is the imaginary unit, i.e., a (non-real) number satisfying .Addition and multiplication of real numbers are defined in such a way that expressions of this type satisfy all field axioms and thus hold for . For example, the distributive law enforces
: It is immediate that this is again an expression of the above type, and

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