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represents a quantity with infinite magnitude, but undetermined complex phase.
Details Examplesopen allclose all Basic Examples (1)Division by 0:
Applications (2)Set up a seemingly "analytic" function that is infinite in the whole left half‐plane:
Plotting shows details of the numerical calculation:
Asymptotics of the LogGamma function at ComplexInfinity:
Properties & Relations (6) Neat Examples (2)Infinite arguments of undetermined phase in all elementary functions:
Behavior of the exponential function at ComplexInfinity shown on the Riemann sphere:
HistoryIntroduced in 1988 (1.0)
Wolfram Research (1988), ComplexInfinity, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexInfinity.html. TextWolfram Research (1988), ComplexInfinity, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexInfinity.html.
CMSWolfram Language. 1988. "ComplexInfinity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComplexInfinity.html.
APAWolfram Language. (1988). ComplexInfinity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComplexInfinity.html
BibTeX@misc{reference.wolfram_2025_complexinfinity, author="Wolfram Research", title="{ComplexInfinity}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexInfinity.html}", note=[Accessed: 12-July-2025 ]}
BibLaTeX@online{reference.wolfram_2025_complexinfinity, organization={Wolfram Research}, title={ComplexInfinity}, year={1988}, url={https://reference.wolfram.com/language/ref/ComplexInfinity.html}, note=[Accessed: 12-July-2025 ]}
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