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Complex Number Calculator

Add, subtract, multiply and divide complex numbers in rectangular and polar forms, with phasor angle in degrees, ideal for power systems and AC circuits.

#complex-number-calculator#phasor-calculator#rectangular-to-polar#polar-to-rectangular#ac-circuit-math
A
B
A
3 + j4
5 ∠ 53.13°
B
1 - j2
2.2361 ∠ -63.43°
A + B
Rectangular
4 + j2
Polar (degrees)
4.4721 ∠ 26.57°

Overview

AC power systems are almost always analysed in the phasor domain. Voltages, currents and impedances become complex numbers: a real (in-phase) part and an imaginary (90° quadrature) part, or equivalently a magnitude and an angle in degrees.

This calculator supports add, subtract, multiply and divide in both Cartesian (a + jb) and polar forms (M ∠ θ°). It is ideal for verifying relay calculations, symmetrical component hand-checks, and unbalanced fault studies.

Tip: keep the angle convention consistent (always degrees in this tool) and double-check division by zero cases — very small denominators can amplify rounding noise in polar form.

How it works

  1. 1. Choose op
    + − × ÷.
  2. 2. Enter A and B
    Each input can be rectangular or polar with angle in degrees.
  3. 3. Read result
    Displayed in both a + jb and M ∠ θ° simultaneously.
  4. 4. Chain
    Reuse outputs as new inputs for impedance cascades or sequence networks.

FAQ

Are angles in radians or degrees?+

Everything in AWGtomm2 uses degrees for practical engineering input.

Can I compute impedances here?+

Yes — rectangular works for R + jX and polar works for magnitude and angle in degrees.

What is j?+

The imaginary unit (√-1). Electrical engineering writes j (instead of i) to avoid confusion with current.