Complex

Complex

is the head used for complex numbers.

Details

  • You can enter a complex number in the form x+Iy.
  • _Complex can be used to stand for a complex number in a pattern.
  • You have to use Re and Im to extract parts of Complex numbers.

Examples

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Basic Examples  (1)

Enter a complex number:

Complex is the Head for complex numbers:

Scope  (9)

Enter a purely imaginary number:

Even though there is no real part it has Head Complex:

The FullForm of a complex number x+Iy is Complex[x,y]:

Enter a complex number using the FullForm:

If the imaginary part is exactly zero, then the result is not Complex:

You have to use Re and Im to extract parts of Complex numbers:

Part does not work:

Enter a complex number with machine-number real and imaginary parts:

It is considered to be a machine number when both its real and imaginary parts are machine numbers:

Enter a complex number with arbitrary-precision real and imaginary parts:

The precision is based on the error in the complex plane:

Enter a complex number with an exact real part and an approximate imaginary part:

_Complex can be used to stand for a complex number in a pattern:

A rule that switches real and imaginary parts:

An alternate definition:

Applications  (1)

Define a function over the complexes by using functions defined over the reals:

Properties & Relations  (3)

Complexes are numbers:

Complexes are atomic objects with no subexpressions:

Use Complexes to indicate assumptions on domain conditions:

Possible Issues  (1)

Numbers entered in the form x+Iy only become Complex numbers on evaluation:

The unevaluated form is expressed in terms of Plus and Times:

Wolfram Research (1988), Complex, Wolfram Language function, https://reference.wolfram.com/language/ref/Complex.html.

Text

Wolfram Research (1988), Complex, Wolfram Language function, https://reference.wolfram.com/language/ref/Complex.html.

BibTeX

@misc{reference.wolfram_2020_complex, author="Wolfram Research", title="{Complex}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Complex.html}", note=[Accessed: 18-January-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_complex, organization={Wolfram Research}, title={Complex}, year={1988}, url={https://reference.wolfram.com/language/ref/Complex.html}, note=[Accessed: 18-January-2021 ]}

CMS

Wolfram Language. 1988. "Complex." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Complex.html.

APA

Wolfram Language. (1988). Complex. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Complex.html