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Complex infinity
This functionality does not run in MATLAB.
complexInfinity
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.
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