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Proposition: Existence of Inverse Complex Numbers With Respect to Addition
For every complex number \(x\in\mathbb C\), there exists an inverse complex number \(x\in\mathbb C\) such that the sum of both numbers equals the complex zero:
\[x+(x)=0.\]
In the following interactive figure, you can experiment with the value of \(x\) (i.e. its position in the complex plane) and see, how it influences the value of \(x\), the inverse complex number with respect to addition:
Table of Contents
Proofs: 1
Mentioned in:
Definitions: 1
Proofs: 2 3
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983