Positive angles are measured counterclockwise from the reference axis 0° and negative angles are measured clockwise from the reference axis.Īs the polar representation of a complex number is based on a right-angled triangle, we can use the Pythagorean theorem to find both the magnitude and the angle of a complex number, which is described below. The length of the phasor vector represents the magnitude of a function and the angle φ represents the angular position of the vector. In electrical engineering and electronics, a phasor (from phase vect or) is a complex number in the form of a vector in the polar coordinate system representing a sinusoidal function that varies with time.

The polar representation consists of the vector magnitude r and its angular position φ relative to the reference axis 0° expressed in the following form: Any complex number can be represented by a displacement along the horizontal axis (real part) and a displacement along the vertical axis (imaginary part).Ī complex number can also be represented on the complex plane in the polar coordinate system. In math, the letter i is used instead of j.Ī complex number z = x + jy = r ∠φ is represented as a point and a vector in the complex planeĬomplex numbers can be visually represented as a vector on the complex plane, which is a modified Cartesian plane, where the horizontal axis is called the real axis Re and displays the real part and the vertical axis is called the imaginary axis Im and displays the imaginary part. We use the letter j in electrical engineering because the letter i is reserved for instantaneous current.

In a complex number x + jy, x is called the real part and y is called the imaginary part. See our Electrical, RF and Electronics calculators and Electrical Engineering Converters.Ī complex number z can be expressed in the form z = x + jy where x and y are real numbers and j is the imaginary unit commonly known in electrical engineering as the j-operator that is defined by the equation j² = –1. Using complex numbers, we can do four arithmetic operations with quantities that have both magnitude and angle, and sinusoidal voltages and other AC circuit quantities are precisely characterized by amplitude and angle. Complex numbers allow mathematical operators with phasors and are very useful in the analysis of AC circuits with sinusoidal currents and voltages. In electrical engineering and electronics, when dealing with frequency-dependent sinusoidal sources and reactive loads, we need not only real numbers, but also complex numbers to be able to solve complex equations.

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