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Proposition: Distributivity Law for Complex Numbers

For arbitrary complex numbers $x,y,z\in\mathbb C$ with the binary operations addition "$+$" and multiplication "$\cdot$", the following distributivity laws hold:

$$\begin{array}{ccl} x\cdot(y+z)&=&(x\cdot y)+(x\cdot z).\quad\quad\text{"left-distributivity property"}\\ (y+z)\cdot x&=&(y\cdot x)+(z\cdot x)\quad\quad\text{"right-distributivity property"},\\ \end{array}$$

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References

Bibliography

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