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

`complexInfinity`

is the only element of the domain `stdlib::CInfinity`

.

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