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 simple to describe. In particular, when the complex

In Rectangular Form a complex number is represented by a point in space on the complex plane. 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.

We review elements of complex number analysis that are useful in AC circuit theory and in optics, in particular in the discussion of diffraction. These applications are usually done using phasors, a concept that skirts the

Complex Numbers H §2 The complex representation offers many mathematical advantages over trigonometric expression for oscillators. Complex numbers arise from imaginary numbers. Since there is no real number solution for √ −1, the imaginary number i is arbitrarily assigned as the solution, i.e., i= √ −1=⇒i2 = −1

phase angles can be used for engineering analysis and real-time tools . This paper lays out the considerations that users should be aware of when handling phase angles, including: 1. Phase angle mathematics and background; 2. The phasor angle reported from a PMU; 3. The phase angle difference calculation problem statement; 4.