This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.


Complex infinity

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.




complexInfinity represents the only non-complex point of the one-point compactification of the complex numbers.

Mathematically, complexInfinity is the north pole of the Riemann sphere, with the unit circle as equator and the point 0 at the south pole.

With respect to arithmetic, complexInfinity behaves like “1/0”. In particular, non-zero complex numbers may be multiplied or divided by complexInfinity or 1/ complexInfinity. Adding complexInfinity to a finite number yields again complexInfinity.

With respect to arithmetical operations, complexInfinity is incompatible with the real infinity.


Example 1

complexInfinity can be used in arithmetical operations with complex numbers. The result in multiplications or divisions is either complexInfinity, 0, or undefined:

3*complexInfinity, I*complexInfinity, 0*complexInfinity;
3/complexInfinity, I/complexInfinity, 0/complexInfinity;
complexInfinity/3, complexInfinity/I;
complexInfinity*complexInfinity, complexInfinity/complexInfinity;

The result in additions is undefined if one of the operands is infinite, and complexInfinity otherwise:

complexInfinity + complexInfinity, infinity + complexInfinity;
3 + complexInfinity, I + complexInfinity, PI + complexInfinity

Symbolic expressions in arithmetical operations involving complexInfinity are implicitly assumed to be different from both 0 and complexInfinity:

delete x:
x*complexInfinity, x/complexInfinity, complexInfinity/x,
x + complexInfinity


complexInfinity is the only element of the domain stdlib::CInfinity.

See Also

MuPAD Functions

Was this topic helpful?