Complex (Mag ∠ Phase)

Shipping

complex_polar

Build a complex array from magnitude and phase: z = mag·(cos φ + i·sin φ)

Signature

Inputs

magnitudeArray|Scalarrequired— Modulus |z| per element; carries the output unit.
phaseArray|Scalarrequired— Argument φ per element, in radians. Must match magnitude in length.

Outputs

zArray— Complex array in rectangular form, inheriting magnitude's unit.

Description

Complex (Mag ∠ Phase) constructs a complex array from a polar description — a modulus magnitude and an argument phase (in radians) — and returns it in rectangular form: $z = mag (cos φ + i sin φ)$ . It is the polar-form counterpart of Complex (Re + Im) (complex_pack), and the natural inverse pairing for Magnitude |z| + Phase ∠z.

The two inputs are combined element-wise: $re_{k} = mag_{k} cos φ_{k}$ and $im_{k} = mag_{k} sin φ_{k}$ . They must be equal length (a mismatch is an error). The output inherits the magnitude input's physical unit. The node is stateless.

Mathematics

z_{k} = mag_{k} e^{i φ_{k}} = mag_{k} cos φ_{k} + i mag_{k} sin φ_{k}

re_{k} = mag_{k} cos φ_{k}, im_{k} = mag_{k} sin φ_{k}

Examples

Recompose a phasor

Wire magnitude $5$ and phase $atan2 (4, 3) \approx 0.9273$ rad. The z output is $3 + 4 i$ (to machine precision) — the inverse of taking magnitude and phase of $3 + 4 i$ .

Unit circle point

Magnitude $1$ with phase $π /2$ produces $0 + 1 i$ — a pure imaginary of unit modulus.

Applications

Reconstructing a complex spectrum from a magnitude spectrum plus a phase spectrum before an inverse FFT.
Synthesizing phasors for AC-circuit or control-system analysis directly from amplitude and phase.
Converting log-magnitude / phase representations back into complex data after phase manipulation.

Neat

Phase is always interpreted in radians — pair it with a Trigonometry or Scale/Offset node if your data is in degrees (multiply by π/180 first).

Because magnitude carries the unit while phase is angular, the output correctly inherits the amplitude's physical dimension (e.g. volts) with the phase treated as dimensionless.

Known issues

The magnitude and phase arrays must be equal length; a length mismatch is rejected with an error.

Phase must be supplied in radians — a degree-valued phase silently yields the wrong rectangular components.