represents a quantity with infinite magnitude, but undetermined complex phase.
ComplexInfinity
represents a quantity with infinite magnitude, but undetermined complex phase.
Details
- ComplexInfinity is converted to DirectedInfinity [].
- In OutputForm , DirectedInfinity [] is printed as ComplexInfinity .
Examples
open all close allBasic Examples (1)
Division by 0:
Scope (4)
Use ComplexInfinity in numerical functions:
ComplexInfinity absorbs finite real, complex, and symbolic quantities:
Do arithmetic with ComplexInfinity :
Use ComplexInfinity as an expansion point for series:
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)
Use Quiet to suppress messages:
ComplexInfinity can be generated by Simplify and FullSimplify :
ComplexInfinity has indeterminate real and imaginary parts:
ComplexInfinity is not a number:
Obtain ComplexInfinity from limits:
ComplexInfinity behaves like a constant in differentiation:
Possible Issues (4)
ComplexInfinity is not a numeric quantity:
ComplexInfinity is a symbol with infinite precision:
ComplexInfinity evaluates to DirectedInfinity :
Use ComplexInfinity with care in boundary conditions of differential equations:
Neat Examples (2)
Infinite arguments of undetermined phase in all elementary functions:
Behavior of the exponential function at ComplexInfinity shown on the Riemann sphere:
See Also
Tech Notes
Related Guides
Related Links
History
Introduced in 1988 (1.0)
Text
Wolfram Research (1988), ComplexInfinity, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexInfinity.html.
CMS
Wolfram Language. 1988. "ComplexInfinity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComplexInfinity.html.
APA
Wolfram 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: 17-November-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: 17-November-2025]}