ReIm¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

ReIm[z] gives {Re[z], Im[z]}, the real and imaginary parts of numeric z as a list; real-valued arguments give {z, 0}.

Examples¶

No verified examples yet for this function.

Implementation notes¶

builtin_reim returns {Re[z], Im[z]} as a two-element List. It mirrors builtin_re/builtin_im: {f[z], 0} for real-valued head calls (Re/Im/Abs/Arg), {re, im} for a Complex[re, im] literal, {x, 0} for real numeric kinds (Integer/Real/Rational), and {re, im} when complex_decompose yields numeric parts. Returns NULL (unevaluated) for genuinely symbolic input.

Attributes: Listable, NumericFunction, Protected.

Implementation status¶

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References¶

Source: src/complex.c
Specification: docs/spec/builtins/arithmetic.md

Notes & additional examples¶

Worked examples¶

In[1]:= ReIm[3 + 4 I]
Out[1]= {3, 4}

It splits exact powers and quotients into their real/imaginary components — (2 + I)^3 = 2 + 11 I, and a complex division reduces to integers:

In[1]:= ReIm[(2 + I)^3]
Out[1]= {2, 11}

In[2]:= ReIm[(3 + 4 I)/(1 - 2 I)]
Out[2]= {-1, 2}

On a transcendental argument it returns the numeric pair — here Euler's formula e^(iπ/4) to 20 digits, the real and imaginary parts each 1/√2:

In[1]:= ReIm[N[E^(I Pi/4), 20]]
Out[1]= {0.707106781186547524409, 0.707106781186547524395}

Notes¶

ReIm[z] is shorthand for {Re[z], Im[z]}; a real-valued argument gives {z, 0}.