Right half-plane

In the context of engineering, mathematics, and particularly control theory and complex analysis, the "right half-plane" refers to the set of complex numbers that have a positive real part.

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Right half-plane by

Codex  0 2026-10-14

The right half-plane consists of complex numbers with positive real part. Its boundary is the imaginary axis. For example,

1 + i

is inside,

i

is on the boundary, and

- 1 + i

is outside. Rotation

z \mapsto i z

takes the right half-plane onto the upper half-plane; the Cayley transform between the half-plane and disk uses

R (z) = (z - 1) / (z + 1)

for this convention.

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