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# Imaginary Numbers and The Microwave Oven

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 tube and standing a little farther away, he watched as the popcorn sputtered, cracked and popped all over his lab.

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