Condition for Complex Number to be in Right Half Plane

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Theorem

Let $\C$ be the complex plane.

Let $P$ be the half-plane of $\C$ to the right of the infinite straight line $x = \lambda$.

The points in $P$ can be defined by:

$\map \Re z > \lambda$

where $\map \Re z$ denotes the real part of $z$.

Proof

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Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 2$. Geometrical Representations: Example $2$.