ABSTRACT
Few radiologists are familiar with the use of complex numbers. However, complex numbers greatly facilitate the expression of several mathematical concepts. Wave functions, such as ultrasound waves, are more easily expressed using complex exponentials. In order to understand complex number system, this chapter introduces some number systems which are more familiar. It provides complicated number systems — nonzero positive integers, positive integers, integers, rational numbers, real numbers, and complex numbers. Complex numbers are integral to most common mathematical description of quantum mechanics. In radiology, complex numbers are used to describe the nuclear magnetic resonance signal. Complex numbers can also be expressed in polar notation. A plane wave is a three-dimensional signal which has a sinusoidal variation of one dimension. The intensity of the wave is not a function of the other two dimensions. These two dimensions represent planes perpendicular to the wave. The effect of tissue on an ultrasound beam is due to two effects — attention and phase shift.
