Conjugate z*

Shipping

conjugate

Complex conjugate z* = re − i·im (negates the imaginary part)

Signature

Inputs

zArray|Complex|Scalarrequired— Complex or real input. A real input conjugates to itself (stays real).

Outputs

zArray— Conjugated complex array (or the unchanged real array), keeping z's unit.

Description

Conjugate z\ returns the complex conjugate of each element: $z^\ = \Re(z) - i\,\Im(z)$ — the real part is untouched and the imaginary part is negated. The output keeps z's physical unit.

A real input conjugates to itself and is returned as a real array (never promoted to complex): $z^{\*} = z$ when $ℑ (z) = 0$ . The node is stateless.

Mathematics

z_{k}^{\*} = ℜ (z_{k}) - i ℑ (z_{k})

z z^{\*} = ∣ z ∣^{2}, real input: z^{\*} = z

Examples

Conjugate a phasor

Feeding $[1 + 2 i]$ gives $[1 - 2 i]$ . A real input $[5]$ returns $[5]$ and stays real (not $5 + 0 i$ ).

Applications

Forming $z\,z^\* = |z|^2$ for power-spectral-density computations.
Building matched filters and cross-correlations in the frequency domain (multiply by the conjugate spectrum).
Enforcing conjugate symmetry when constructing a real-valued signal's spectrum.

Neat

A real input short-circuits: conj returns the array as real (None imaginary buffer) rather than allocating a zero imaginary column — conjugation never widens a real value to complex.

Conjugation is a metadata-preserving sign flip on a single buffer, so it is essentially free relative to the memory it touches.