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By Tony R. Kuphaldt

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COMPLEX NUMBERS • In rectangular notation, the first quantity is the ”real” component (horizontal dimension of vector) and the second quantity is the ”imaginary” component (vertical dimension of vector). The imaginary component is preceded by a lower-case ”j,” sometimes called the j operator. • Both polar and rectangular forms of notation for a complex number can be related graphically in the form of a right triangle, with the hypotenuse representing the vector itself (polar form: hypotenuse length = magnitude; angle with respect to horizontal side = angle), the horizontal side representing the rectangular ”real” component, and the vertical side representing the rectangular ”imaginary” component.

So are X-rays and ”gamma” ray radiation. The only difference between these kinds of electromagnetic radiation is the frequency of their oscillation (alternation of the electric and magnetic fields back and forth in polarity). By using a source of AC voltage and a special device called an antenna, we can create electromagnetic waves (of a much lower frequency than that of light) with ease. An antenna is nothing more than a device built to produce a dispersing electric or magnetic field. Two fundamental types of antennae are the dipole and the loop: Basic antenna designs DIPOLE LOOP While the dipole looks like nothing more than an open circuit, and the loop a short circuit, these pieces of wire are effective radiators of electromagnetic fields when connected to AC sources of the proper frequency.

Subtraction is similar. • To multiply complex numbers in polar form, multiply the magnitudes and add the angles. To divide, divide the magnitudes and subtract one angle from the other. 7 More on AC ”polarity” Complex numbers are useful for AC circuit analysis because they provide a convenient method of symbolically denoting phase shift between AC quantities like voltage and current. However, for most people the equivalence between abstract vectors and real circuit quantities is not an easy one to grasp.

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