Modulus Larger than Real Part

Theorem
Let $z \in \C$ be a complex number.

Then the modulus of $z$ is larger than the real part $\map \Re z$ of $z$:
 * $\cmod z \ge \size {\map \Re z}$

Proof
By the definition of a complex number, we have:
 * $z = \map \Re z + i \map \Im z$

Then:

Also see

 * Modulus Larger than Imaginary Part