Modulus Larger than Real Part and Imaginary Part
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Theorem
Let $z \in \C$ be a complex number.
Let $\operatorname{Re} \left({z}\right)$ denote the real part of $z$, and $\operatorname{Im} \left({z}\right) $ the imaginary part of $z$.
Then:
Modulus Larger than Real Part
- $\cmod z \ge \size {\map \Re z}$
Modulus Larger than Imaginary Part
- $\cmod z \ge \size {\map \Im z}$