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:


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:

Proofs: 1

Definitions: 1
Proofs: 2 3

Thank you to the contributors under CC BY-SA 4.0!




  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983