Phase ∠z

Shipping

phase

Element-wise argument arg(z) = atan2(im, re) in radians

Signature

Inputs

zArray|Complex|Scalarrequired— Complex or real input. A real input yields 0 for re ≥ 0 and π for re < 0.

Outputs

phaseArray— Real array of arguments in radians (unit = "rad").

Description

Phase ∠z returns the element-wise argument (angle) of a complex array: $ar g (z) = atan2 (ℑ z, ℜ z)$ , in radians on $(- π, π]$ . The output is always tagged with the unit rad.

A real input is handled by convention: the phase is $0$ where $ℜ (z) \geq 0$ and $π$ where $ℜ (z) < 0$ (a negative real number lies on the negative real axis). The node is stateless.

Mathematics

ar g (z_{k}) = atan2 (ℑ z_{k}, ℜ z_{k}) \in (- π, π]

real input: ar g (z_{k}) = {0 π ℜ z_{k} \geq 0 ℜ z_{k} < 0

Examples

Angle of a phasor

Feeding $[0 + 1 i]$ gives $[π /2]$ ; feeding $[3 + 4 i]$ gives $[atan2 (4, 3)] \approx [0.9273]$ rad.

Phase spectrum

Pair with Magnitude |z| on a complex FFT output to obtain the (magnitude, phase) polar description of a spectrum.

Applications

Extracting the phase spectrum from a complex FFT result.
Computing instantaneous phase of an analytic signal for phase-unwrapping or frequency estimation.
Measuring the phase difference between two phasors in AC / control analysis.

Neat

Uses atan2 (not atan), so the full four-quadrant angle on (-π, π] is recovered without sign ambiguity.

The output is explicitly stamped 'rad' regardless of the input's unit — phase is dimensionally an angle, not the amplitude's unit.

Known issues

The result is wrapped to (-π, π]; use a downstream unwrap step if a continuous phase across ±π boundaries is required.

arg(0) is 0 by convention here (the phase of an exact zero is undefined mathematically).