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complexInfinity -- complex infinity

Introduction

complexInfinity represents the only non-complex point of the one-point compactification of the complex numbers.

Related Functions

infinity

Details

Example 1

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

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