# 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

## Sources

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