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CIRCUMFERENCE
. See
CIRCLES
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COMPLEX NUMBERS
Complex numbers are numbers expressed in the form a + bi, where a is the
real number component and b is the imaginary number component. The number
i is the square root of negative 1: i
=
√
−1. Numbers in the physical world are
often represented by their real number component, such as in measurement,
money, and time. For example, a mile is a unit of measurement that is equivalent
to 5,280 feet. As a complex number, this measurement would be 5,280 + 0i feet.
However, the expression in complex form does not produce any additional mean-
ing if the imaginary number component is equal to zero. Therefore, complex
numbers are useful when the imaginary number component is nonzero.
There are several instances in which imaginary numbers are important in the
physical world. For example, some circuits have unexpected changes of voltage
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