Proof
(related to Proposition: Algebraic Structure of Complex Numbers Together with Addition and Multiplication)
The set of complex numbers \(\mathbb C\), together with the specific addition operation "\(+\)", and the specific multiplication operation "\(\cdot\)", forms the field the algebraic structure \((\mathbb C, + , \cdot)\). This is because:
 We have shown that the set \((\mathbb C, + )\) is a commutative group.
 We have shown that the set \((\mathbb C^*, \cdot )\) is a commutative group, in which \(\mathbb C^*\) denotes all nonzero complex numbers.
 We have shown that the set \((\mathbb C^*, \cdot )\) is a commutative group, in which \(\mathbb C^*\) denotes all nonzero complex numbers.
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983