In Polar Form a complex number is represented by a line whose length is the amplitude and by the phase angle. In Exponential Form a complex number is represented by a line and corresponding angle that uses the base of the natural logarithm.

Every nonzero complex number can be expressed in terms of its magnitude and angle. This angle is sometimes called the phase or argument of the complex number. Although formulas for the angle of a complex number are a bit complicated, the angle has some properties that are …

Phasors will be used again in EECS 215 and 314. It also includes a brief primer on complex numbers and their manipulations. A. Table of contents by sections: 1. Abstract (you’re reading this now) 2. Complex numbers: Magnitude, phase, real and imaginary parts 3. Complex numbers: Polar-to-Rectangular conversion and vice-versa 4.

Dec 1, 2016 · Phase angl e – The angle of a vector in respect to the the right hand horizontal axis. The most standard electrical Phase sequence is Positive ABC, which means that phasors rotate around the phasor diagram counter clockwise.

In this chapter we use what we have learned about complex numbers and the function ej θ to develop a phasor calculus for representing and manipulating sinusoids.

An alternative form of representation of a complex number is the expo-nential form Aejf, where A is the magnitude and f is the phase angle.To con-vert from one form to another, we first recall that

We can thus represent a complex number z1 in terms of a real and imaginary component (rectangular coordinates), or in terms of a mag-nitude, jz1j, and a phase angle \z1 (polar coordinates).

The phase angle is defined graphically from the x-y plane interpretation: it is the counterclockwise angle from the positive x-axis to the vector represented by the complex number.

The key mathematical idea behind this is the representation of complex numbers as a magnitude and phase and algebra of complex numbers that follows. We’ll start there, and then return to complex impedance and an application of it.

This angle is sometimes called the phase or argument of the complex number. Although formulas for the angle of a complex number are a bit complicated, the angle has some properties that are simple to describe.