A Phasor is a Complex Number representing a Sinusoidal quantity, usually in Exponential_function form. They are used in engineering to simplify computations involving sinusoids, where they can often reduce a Differential_equation problem to an algebraic one.

generally a sinewave can be expressed in the form (the reason for using cos rather than sin will become apparent later)

where

• y is the quanitity that is varying with time
• φ is a constant offset known as the phase angle
• A is the peak value (aplitude) of the waveform
• ω is the angular frequency ω = 2πf where f is frequency.
• t is time.

this can be expressed as

where

• j is the imaginary unit
• re() represents the real part of a complex number

which in turn can be changed using Euler's formula into

Ae^φ is a complex number encoding the magnitude and phase of the sinewave known as a phasor. Phasors are often written in the form A∠φ (∠ is the angle sign U+220).

In electronic circuit analysis, a phasor is a quantity with magnitude and phase used in the analysis of an AC circuit that uses a single frequency of sine wave.

The magnitude of a phasor represents voltage or current. The angle represents the phase with relation to a fixed reference (usually one of the circuit's power supplies).

A positive angle represents leading; a negative angle represents lagging.

Phasors can be represented in either cartesian or exponential form.

Ohm's law can be extended to V=IZ where V and I are phasors represented as complex numbers and Z is the complex impedance of the component.

Other circuit analysis techniques that work for DC voltages, currents and resistances work for phasor voltage and current with complex impedances.