The SMITH CHART is based on complex numbers and is used in electronic to find real and imanginary impedences. It is loosely based on the Mobius transform and is the formula w=(z-1)/(z+1)
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It need not be. For example, a complex number as a percent of most other complex numbers, or any real number, will not be a real number.
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The absolute value of a complex number is the magnitude of the number, which is found from sqrt(a² + b²) for the complex number a + bi
No. A complex number is a number that has both a real part and an imaginary part. Technically, a pure imaginary number ... which has no real part ... is not a complex number.
A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.