Addition of Real and Imaginary Parts

Theorem
Let $z_0, z_1 \in \C$ be two complex numbers.

Then:


 * $\map \Re {z_0 + z_1} = \map \Re {z_0} + \map \Re {z_1}$

and:


 * $\map \Im {z_0 + z_1} = \map \Im {z_0} + \map \Im {z_1}$

Here, $\map \Re {z_0}$ denotes the real part of $z_0$, and $\map \Im {z_0}$ denotes the imaginary part of $z_0$.

Proof
We have: