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Boilerplate in preface
{{Math-m}}
{{Math-m}}
The '''complex numbers''' are a set of numbers which have important applications in the analysis of periodic, oscillatory, or wavelike phenomena. They are the 5<sup>th</sup> item in this hierarchy of types of [[number]]s:
The '''complex numbers''' are a set of numbers which have important applications in the analysis of periodic, oscillatory, or wavelike phenomena. Mathematicians denote the set of complex numbers with an ornate capital letter: <math>\mathbb{C}</math>. They are the 5<sup>th</sup> item in this hierarchy of types of [[number]]s:
*The "[[natural number]]s", 1, 2, 3, ... (There is controversy about whether zero should be included. It doesn't matter.)
*The "[[natural number]]s", 1, 2, 3, ... (There is controversy about whether zero should be included. It doesn't matter.)
*The "complex numbers, which give solutions to polynomial equations
*The "complex numbers, which give solutions to polynomial equations
A complex number is composed of two parts, or components—a ''[[Real number|real]]'' component and an ''imaginary'' component. Each of these components is an ordinary (that is, real) number. The complex numbers form an "extension" of the real numbers: If the imaginary component of a complex number is zero, that number is essentially identical to the real number that is its real component.
A complex number is composed of two parts, or components—a ''real'' component and an ''imaginary'' component. Each of these components is an ordinary (that is, real) number. The complex numbers form an "extension" of the real numbers: If the imaginary component of a complex number is zero, that number is essentially identical to the real number that is its real component.
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