Complexes

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`Complexes`

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Complexes

represents the domain of complex numbers, as in x∈Complexes.

Details

x∈Complexes evaluates immediately only if x is a numeric quantity.
Simplify[expr∈Complexes] can be used to try to determine whether an expression corresponds to a complex number.
The domain of real numbers is taken to be a subset of the domain of complex numbers.
Complexes is output in StandardForm or TraditionalForm as . This typeset form can be input using comps.

Examples

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Basic Examples (3)Summary of the most common use cases

is a complex number:

In[1]:=1

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https://wolfram.com/xid/0c11oly-gfxecg

Out[1]=1

Exponential of a complex number is a complex number:

In[1]:=1

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https://wolfram.com/xid/0c11oly-iqwka5

Out[1]=1

Find complex numbers that make an inequality well defined and True:

In[1]:=1

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https://wolfram.com/xid/0c11oly-eqszwi

Out[1]=1

Scope (2)Survey of the scope of standard use cases

Specify that all variables should be considered complex, even if they appear in inequalities:

In[1]:=1

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https://wolfram.com/xid/0c11oly-d1s04z

Out[1]=1

By default, Reduce considers all variables that appear in inequalities to be real:

In[2]:=2

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https://wolfram.com/xid/0c11oly-zou29

Out[2]=2

For every real number y there exists a complex number whose square is real and less than y:

In[3]:=3

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https://wolfram.com/xid/0c11oly-b00i4q

Out[3]=3

By default, Resolve considers all variables that appear in inequalities to be real:

In[4]:=4

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https://wolfram.com/xid/0c11oly-iud0w

Out[4]=4

TraditionalForm of formatting:

In[1]:=1

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https://wolfram.com/xid/0c11oly-4xdcq9

Properties & Relations (2)Properties of the function, and connections to other functions

Complexes contains Reals, Algebraics, Rationals, Integers, and Primes:

In[1]:=1

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https://wolfram.com/xid/0c11oly-culh0e

Out[1]=1

Infinite quantities are not considered part of the Complexes:

In[1]:=1

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https://wolfram.com/xid/0c11oly-28e7i

Out[1]=1

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