complexInfinity
--
complex infinitycomplexInfinity
represents the only non-complex point
of the one-point compactification of the complex numbers.
complexInfinity
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
.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;
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
complexInfinity
is the only element of the domain stdlib::CInfinity
.