complexInfinity --
complex infinity
IntroductioncomplexInfinity represents the only non-complex point
of the one-point compactification of the complex numbers.
Related
Functions
DetailscomplexInfinity is the north pole of
the Riemann sphere, with the unit circle as equator and the point
0 at the south pole.complexInfinity behaves
like ``1/0''. In particular, nonzero complex numbers may
be multiplied or divided by complexInfinity or
1/complexInfinity. Adding complexInfinity to
a nonzero number yields undefined.complexInfinity is incompatible with the real infinity.
Example
1complexInfinity 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;
complexInfinity, complexInfinity, undefined
0, 0, 0
complexInfinity, complexInfinity
complexInfinity, undefined
Symbolic expressions in multiplications or divisions
involving complexInfinity are implicitly assumed to be
different from both 0 and
complexInfinity:
>> delete x: x*complexInfinity, x/complexInfinity, complexInfinity/x
complexInfinity, 0, complexInfinity
The result in additions is always undefined:
>> 3 + complexInfinity, I + complexInfinity, x + complexInfinity
undefined, undefined, undefined
BackgroundcomplexInfinity is the only element of the domain stdlib::CInfinity.