Re

The real part of a complex number. An alias for Real, the preferred name.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimRe↗Wolfram LanguageRe!↗

Re(complex | infinity) -> numberthe real part of $z$; distributes over a symbolic real value unchanged.

SageMathreal_part(complex | infinity)SymPyre(complex | infinity)mpmathre(complex | infinity)

Typed signatures

Type	Package	Applies
(complex | infinity) -> number	compute-engine	always

Domain: Compute engine

Details

• A Gaussian integer is a complex number with integer parts, so Re and Imaginary read its two coordinates; there is no separate head for them.

Plot

ComplexPlot

real slice

Examples

Basic #

$\mathrm{Re}(3+4i) = 3$

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In$\mathrm{Re}(3+4i)$Out$3$

Re of a real number is itself

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In$\mathrm{Re}(5)$Out$5$

Re of $\pi$ is $\pi$, a real symbolic constant

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In$\mathrm{Re}(π)$Out$π$

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In$\Re(2+3i)$Out$2$

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In$\Re(2e^{(1/3)i π})$Out$1$

Scope #

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In$\Re(\frac{3}{2}+\frac{4}{5}i)$Out$\frac{3}{2}$

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In$N(\Re(e+i π), 25)$Out$2.718\,281\,828\,459\,045\,235\,360\,287$

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In$\Re(\frac{41}{25}-2i)$Out$\frac{41}{25}$

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In$\Re(\bigl\lbrack\bigl\lbrack1, u\bigr\rbrack, \bigl\lbrack v, -i\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack1, \Re(u)\bigr\rbrack, \bigl\lbrack\Re(v), 0\bigr\rbrack\bigr\rbrack$

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In$\Re(0)$Out$0$

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In$\Re(∞)$Out$∞$

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In$\Re(∞i)$Out$\operatorname{Indeterminate}$

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In$\Re(\tilde∞)$Out$\operatorname{Indeterminate}$

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In$\mathrm{PiecewiseExpand}(\mathrm{Re}(i x), -2\lt x\lt2)$Out$\Re(i x)$

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In$\mathrm{Simplify}(\mathrm{Re}(x), x\gt0)$Out$\Re(x)$

A Gaussian integer is a complex number with integer parts: $(2+i)(1+3i)=-1+7i$

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In$\mathrm{Re}((2+i)(1+3i))$Out$-1$

Properties #

Re of a symbolic value stays unevaluated

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In$\mathrm{Re}(x)$Out$\Re(x)$

A real number is its own real part

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In$\Re(1)$Out$1$

Known value · Wolfram MathematicalFunctionData, Re

Negative reals are unchanged

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In$\Re(-1)$Out$-1$

Known value · Wolfram MathematicalFunctionData, Re

Likewise for $-i$

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In$\Re(-i)$Out$0$

Known value · Wolfram MathematicalFunctionData, Re

Only the real part of $1+i$ remains

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In$\Re(1+i)$Out$1$

Known value · Wolfram MathematicalFunctionData, Re

The sign of the real part is kept: $-1$

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In$\Re(-1+i)$Out$-1$

Known value · Wolfram MathematicalFunctionData, Re

Both imaginary signs give $-1$ here

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In$\Re(-1-i)$Out$-1$

Known value · Wolfram MathematicalFunctionData, Re

Flipping the imaginary sign leaves the real part alone

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In$\Re(1-i)$Out$1$

Known value · Wolfram MathematicalFunctionData, Re

The imaginary $\sqrt3 i$ drops out, leaving 1

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In$\Re(1+\sqrt{3}i)$Out$1$

Known value · Wolfram MathematicalFunctionData, Re

Real part $-1$ from $-1+\sqrt3 i$

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In$\Re(\sqrt{3}i-1)$Out$-1$

Known value · Wolfram MathematicalFunctionData, Re

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In$\bigl\lbrack\Re(xe^{(1/5)i π}), \Re(2x+i)\bigr\rbrack$Out$\bigl\lbrack\Re(x×(\frac{1}{4}+\frac{\sqrt{5}}{4}+\frac{2^{1/2}}{4}i\sqrt{5-5^{1/2}})), \Re(2x+i)\bigr\rbrack$

The imaginary part does not affect $-\sqrt3$

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In$\Re(-i-\sqrt{3})$Out$-\sqrt{3}$

Known value · Wolfram MathematicalFunctionData, Re

Real part of a point at angle $240^\circ$ is $-1$

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In$\Re(-\sqrt{3}i-1)$Out$-1$

Known value · Wolfram MathematicalFunctionData, Re

A point at angle $-60^\circ$ has real part 1

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In$\Re(1-\sqrt{3}i)$Out$1$

Known value · Wolfram MathematicalFunctionData, Re

Real part $\sqrt3$ from $\sqrt3 - i$

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In$\Re(\sqrt{3}-i)$Out$\sqrt{3}$

Known value · Wolfram MathematicalFunctionData, Re

A real integer is returned as is

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In$\Re(2)$Out$2$

Known value · Wolfram MathematicalFunctionData, Re

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In$\Re(i)$Out$0$

Known value · Wolfram MathematicalFunctionData, Re

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In$\Re(\sqrt{3}+i)$Out$\sqrt{3}$

Known value · Wolfram MathematicalFunctionData, Re

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In$\Re(i-\sqrt{3})$Out$-\sqrt{3}$

Known value · Wolfram MathematicalFunctionData, Re

About

Examples	35
Checked against	Wolfram Language 31 agree4 differSageMath 30 agree1 differ1 unevaluated1 errorSymPy 31 agree1 differ1 unevaluatedmpmath 29 agreeJulia 23 agree2 error
Crosswalk	FungrimWolfram LanguageSageMathSymPympmath

Implementation

mappedsympypackages/oracle/src/mappings.ts

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

See also: Imaginary, Conjugate, Argument