represents the domain of complex numbers, as inx∈Complexes.
Complexes
represents the domain of complex numbers, as inx∈Complexes.
Details
- x∈Complexes evaluates immediately only ifx 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 inStandardForm orTraditionalForm as
![TemplateBox[{}, Complexes]](/image.pl?url=http%3a%2f%2freference.wolfram.com%2flanguage%2fref%2fFiles%2fComplexes.en%2f1.png&f=jpg&w=240 "TemplateBox[{}, Complexes]")
. This typeset form can be input using
comps
.
Examples
open allclose allBasic Examples (3)
Exponential of a complex number is a complex number:
Find complex numbers that make an inequality well defined andTrue:
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 numbery there exists a complex number whose square is real and less thany:
By default,Resolve considers all variables that appear in inequalities to be real:
TraditionalForm of formatting:
Related Guides
History
Introduced in 1999(4.0) |Updated in 2017(11.2)
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_2025_complexes, author="Wolfram Research", title="{Complexes}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Complexes.html}", note=[Accessed: 29-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_complexes, organization={Wolfram Research}, title={Complexes}, year={2017}, url={https://reference.wolfram.com/language/ref/Complexes.html}, note=[Accessed: 29-November-2025]}
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