Imaginary numbers have had a great effect whether direct or indirect on the microwave oven. Although the concept has come out of left field, there is still a plausible explanation for their influence on the microwave oven. The fact remains that complex numbers have much less direct relevance to real-world quantities than other numbers do. An imaginary number could not be used as a measurement of how much water is in a bottle, or how far a kite has traveled, or how many fingers you have. There are a few real world quantities for which complex numbers are the natural model. The strength of an electromagnetic field is one example.
The field has both an electric and a magnetic component, so it takes a pair of real numbers (one for the intensity of the electric field, one for the intensity of the magnetic field) to describe the field strength. This pair of real numbers can be thought of as a complex number, and it turns out that the rule of multiplication of complex numbers is pertinent to the physics of an electromagnetic field. Although direct applications of complex numbers to the real world are small, their indirect applications are many. Many properties related to real numbers only become clear when the real numbers are thought of as sitting inside the complex number system. Therefore, complex numbers aid in the understanding even of things that are described by ordinary, familiar real numbers. Like many of today's great inventions, the microwave oven was a by-product of another technology.
During a radar-related research project around 1946, Dr. Percy Spencer, a self-taught engineer with the Raytheon Corporation, noticed something very unusual. He was testing a new vacuum tube called a magnetron, when he discovered that the candy bar in his pocket had melted. This intrigued Dr. Spencer, so he tried another experiment.
This time he placed some popcorn kernels near the tub and standing a little farther away, he watched as the popcorn sputtered, cracked and popped all over his lab. The next morning, Dr. Spencer decided to put the magnetron tube near an egg. The rapid temperature rise within the egg was causing tremendous internal pressure.
The quaking egg splattered all over the lab station. The melted candy bar, the popcorn, and now the exploding egg, were all attributable to exposure to low-density microwave energy. Therefore, if an egg can be cooked that quickly, why not other foods Dr. Spencer made a metal box with an opening into which he fed microwave power. The energy entering the box was unable to escape, thereby creating a higher density electromagnetic field.
When food was placed in the box and microwave energy fed in, the temperature of the food rose very rapidly. Dr. Spencer had invented what was to revolutionize cooking, and form the basis of a multimillion dollar industry, the microwave oven. Dr. Spencer used the complex number system to quantify the electric and magnetic components in the electromagnetic field used in microwave ovens to heat foods. This great advancement made it easier to prepare foods for everyday consumption.
Although its practical uses have been few and far between, imaginary numbers have made a lasting impression on our everyday lives.