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complexInfinity 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.
With respect to arithmetic,
1/0”. In particular, non-zero
complex numbers may be multiplied or divided by
a finite number yields again
With respect to arithmetical operations,
incompatible with the real
complexInfinity can be used in arithmetical
operations with complex numbers. The result in multiplications or
divisions is either
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,
complexInfinity + complexInfinity, infinity + complexInfinity; 3 + complexInfinity, I + complexInfinity, PI + complexInfinity
Symbolic expressions in arithmetical operations involving
implicitly assumed to be different from both
delete x: x*complexInfinity, x/complexInfinity, complexInfinity/x, x + complexInfinity
complexInfinity is the only element of the domain