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"ComplexNumber" (Interpreter Type)

Complex number in a standard format.

Details

Allowed Forms

  • The real and imaginary parts can be in the number formats allowed by "Number".

Restriction Specifications

Options

  • The following options can be used for the real and imaginary parts:
  • DigitBlockInfinitynumber of digits between breaks
    NumberPoint"."decimal point string
    NumberSeparator{",",""}string to insert at breaks between blocks
    NumberSigns{"-",""}strings to use for signs of negative and positive numbers

Interpretation

Examples

Basic Examples  (5)

Interpret complex numbers:

Wolfram Language code: Interpreter["ComplexNumber"]["3I"]
Wolfram Language code: Interpreter["ComplexNumber"]["-.5i+4"]

Use the options to customize the number format:

Wolfram Language code: Interpreter["ComplexNumber", NumberSigns -> {"n", "p"}]["nI p15"]
Wolfram Language code: Interpreter["ComplexNumber", NumberSeparator -> "#"]["10#000i"]
Wolfram Language code: Interpreter["ComplexNumber", NumberPoint -> ","]["1+7,3i"]

Restrict the result to the unit circle:

Wolfram Language code: Interpreter[Restricted["ComplexNumber", Circle[]]][" -i"]
Wolfram Language code: Interpreter[Restricted["ComplexNumber", Circle[]]]["1 - i"]

Restrict the result to any region of the complex plane:

Wolfram Language code: Interpreter[Restricted["ComplexNumber", ImplicitRegion[x^2 + y^2 ≤ 1, {x, y}]]][" -i"]
Wolfram Language code: Interpreter[Restricted["ComplexNumber", InfiniteLine[{0, 0}, {1, -1}]]][".4 - i .4"]

Set the precision:

Wolfram Language code: Interpreter[Restricted["ComplexNumber", Automatic, 3]]["1.23456i+4.56789"]

Otherwise, $MachinePrecision is implied:

Wolfram Language code: Interpreter["ComplexNumber"]["1.23456i"]//Precision