Complex Numbers in Real Life
Jefferson Community College
June 25, 2009
Complex numbers became more prominent in the 16th century, when closed formulas for the roots of cubic and quartic polynomials were discovered by Italian mathematicians. Imaginary numbers were defined in 1572 by Rafael Bombelli, an Italian mathematician who wrote an influential algebra text and made free use of both negative numbers and complex numbers. Bombelli solved equations, and he introduced +i and -i and described how they both worked in Algebra, thus defining imaginary numbers.
One of the most familiar examples where we use imaginary numbers, or "complex numbers" as they are sometimes called, is from electrical engineering, where imaginary numbers are used to keep track of the amplitude and phase of an electrical oscillation, such as an audio signal, or the electrical voltage and current that power electrical appliances.
Closely related to the electrical engineering example is the use of complex numbers in signal processing, which has applications to telecommunications (cellular phone), radar (which assists the navigation of airplanes), and even biology (in the analysis of firing events from neurons in the brain).
Another important application of complex numbers is their use in a field of physics called quantum mechanics. Although quantum mechanics is not an everyday subject, it is extremely important in many common applications with which we are familiar. Imaginary (complex) numbers help form the descriptions of electronic states in materials (which lead to applications in optics - fluorescent and incandescent lights and CCD cameras, even the description of polarization for polarized sunglasses), electronics (transistors and other semiconductor devices, as well as magnetism, which has applications to magnetic disk drives and other storage devices), and chemistry (the covalent bonding between atoms).