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What are real-life uses of imaginary numbers?

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According to the university of Toronto, there are a variety of uses for imaginary numbers in the real world, most notably in the fields of electrical engineering and measuring natural phenomena. An electromagnetic field, for example, requires imaginary numbers to measure because the strength of the field is determined by both electrical and magnetic components that must be combined into a single complex imaginary number to get an accurate measurement.

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According to Drexel University, imaginary numbers are further used when measuring phenomena that occur in nature such as the disruption created when water flows around an object. Imaginary numbers are quite useful in many situations where more than one force is acting simultaneously, and the combined output of these forces needs to be measured. These forces can be measured using conventional means, but combining the forces using imaginary numbers makes getting an accurate measurement much easier.

An imaginary number is a real number that has been multiplied by i, an imaginary unit that is equivalent to the square root of -1. This means that imaginary numbers are essentially negative perfect squares. Since it is otherwise impossible to achieve a negative square root through standard multiplication, imaginary numbers become necessary to make certain equations balance properly.

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