Complexes

Complexes

represents the domain of complex numbers, as in x∈Complexes.

Details

  • x∈Complexes evaluates immediately only if x is a numeric quantity.
  • Simplify[expr∈Complexes] can be used to try to determine whether an expression corresponds to a complex number.
  • The domain of real numbers is taken to be a subset of the domain of complex numbers.
  • Complexes is output in StandardForm or TraditionalForm as TemplateBox[{}, Complexes]. This typeset form can be input using comps.

Examples

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Basic Examples  (3)

is a complex number:

Exponential of a complex number is a complex number:

Find complex numbers that make an inequality well defined and True:

Scope  (2)

Specify that all variables should be considered complex, even if they appear in inequalities:

By default, Reduce considers all variables that appear in inequalities to be real:

For every real number y there exists a complex number whose square is real and less than y:

By default, Resolve considers all variables that appear in inequalities to be real:

TraditionalForm of formatting:

Properties & Relations  (2)

Complexes contains Reals, Algebraics, Rationals, Integers, and Primes:

Infinite quantities are not considered part of the Complexes:

Wolfram Research (1999), Complexes, Wolfram Language function, https://reference.wolfram.com/language/ref/Complexes.html (updated 2017).

Text

Wolfram Research (1999), Complexes, Wolfram Language function, https://reference.wolfram.com/language/ref/Complexes.html (updated 2017).

CMS

Wolfram Language. 1999. "Complexes." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Complexes.html.

APA

Wolfram Language. (1999). Complexes. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Complexes.html

BibTeX

@misc{reference.wolfram_2024_complexes, author="Wolfram Research", title="{Complexes}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Complexes.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_complexes, organization={Wolfram Research}, title={Complexes}, year={2017}, url={https://reference.wolfram.com/language/ref/Complexes.html}, note=[Accessed: 22-December-2024 ]}