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Wolfram Language & System Documentation Center
ReImPlot
  • See Also
    • AbsArgPlot
    • ComplexListPlot
    • ComplexPlot
    • ComplexPlot3D
    • ReIm
    • AbsArg
    • Plot
    • ParametricPlot
  • Related Guides
    • Complex Visualization
    • Function Visualization
    • Functions of Complex Variables
    • See Also
      • AbsArgPlot
      • ComplexListPlot
      • ComplexPlot
      • ComplexPlot3D
      • ReIm
      • AbsArg
      • Plot
      • ParametricPlot
    • Related Guides
      • Complex Visualization
      • Function Visualization
      • Functions of Complex Variables

ReImPlot[f,{x,xmin,xmax}]

generates a plot of Re[f] and Im[f] as functions of x∈ from xmin to xmax.

ReImPlot[{f1,f2,…},{x,xmin,xmax}]

plots several functions.

ReImPlot[{…,w[fi],…},…]

plots fi with features defined by the symbolic wrapper w.

ReImPlot[…,{x}∈reg]

takes the variable x to be in the geometric region reg.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Sampling  
Labeling and Legending  
Presentation  
Options  
ClippingStyle  
ColorFunction  
ColorFunctionScaling  
Show More Show More
Exclusions  
ExclusionStyle  
Filling  
FillingStyle  
MaxRecursion  
Mesh  
MeshFunctions  
MeshShading  
MeshStyle  
PerformanceGoal  
PlotHighlighting  
PlotLabel  
PlotLabels  
PlotLegends  
PlotPoints  
PlotRange  
PlotStyle  
PlotTheme  
RegionFunction  
ReImLabels  
ReImStyle  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • AbsArgPlot
    • ComplexListPlot
    • ComplexPlot
    • ComplexPlot3D
    • ReIm
    • AbsArg
    • Plot
    • ParametricPlot
  • Related Guides
    • Complex Visualization
    • Function Visualization
    • Functions of Complex Variables
    • See Also
      • AbsArgPlot
      • ComplexListPlot
      • ComplexPlot
      • ComplexPlot3D
      • ReIm
      • AbsArg
      • Plot
      • ParametricPlot
    • Related Guides
      • Complex Visualization
      • Function Visualization
      • Functions of Complex Variables

ReImPlot

ReImPlot[f,{x,xmin,xmax}]

generates a plot of Re[f] and Im[f] as functions of x∈ from xmin to xmax.

ReImPlot[{f1,f2,…},{x,xmin,xmax}]

plots several functions.

ReImPlot[{…,w[fi],…},…]

plots fi with features defined by the symbolic wrapper w.

ReImPlot[…,{x}∈reg]

takes the variable x to be in the geometric region reg.

Details and Options

  • ReImPlot evaluates f at different values of x to create smooth curves of the form {x,Re[f[x]]} and {x,Im[f[x]]}.
  • Gaps are left at any x where the fi evaluate to non-numeric values.
  • The region reg can be any RegionQ object in 1D.
  • ReImPlot treats the variable x as local, effectively using Block.
  • ReImPlot has attribute HoldAll and evaluates f only after assigning specific numerical values to x.
  • In some cases, it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to x.
  • Wrappers apply to both Re[f] and Im[f].
  • The following wrappers w can be used for the fi:
  • Annotation[fi,label]provide an annotation for the fi
    Button[fi,action]evaluate action when the curve for fi is clicked
    Callout[fi,label]label the function with a callout
    Callout[fi,label,pos]place the callout at relative position pos
    EventHandler[fi,events]define a general event handler for fi
    Highlighted[fi,effect]dynamically highlight fi with an effect
    Highlighted[fi,Placed[effect,pos]]statically highlight fi with an effect at position pos
    Hyperlink[fi,uri]make the function a hyperlink
    Labeled[fi,label]label the function
    Labeled[fi,label,pos]place the label at relative position pos
    Legended[fi,label]identify the function in a legend
    PopupWindow[fi,cont]attach a popup window to the function
    StatusArea[fi,label]display in the status area on mouseover
    Style[fi,styles]show the function using the specified styles
    Tooltip[fi,label]attach a tooltip to the function
    Tooltip[fi]use functions as tooltips
  • Wrappers w can be applied at multiple levels:
  • w[fi]wrap the fi
    w[{f1,…}]wrap a collection of fi
    w1[w2[…]]use nested wrappers
  • Callout, Labeled and Placed can use the following positions pos:
  • Automaticautomatically placed labels
    Above, Below, Before, Afterpositions around the curve
    xnear the curve at a position x
    Scaled[s]scaled position s along the curve
    {s,Above},{s,Below},…relative position at position s along the curve
    {pos,epos}epos in label placed at relative position pos of the curve
  • ReImPlot has the same options as Plot, with the following additions and changes: [List of all options]
  • ReImLabels Automatichow to annotate the real and imaginary components
    ReImStyle Automatichow to style the real and imaginary components
    PlotStyle Automatichow to style individual functions fi
  • Possible settings for ClippingStyle are:
  • Automaticuse a dotted line for the clipped portion
    Noneomit the clipped portion of the curve
    styleuse style for the clipped portion
  • With the default settings Exclusions->Automatic and ExclusionsStyle->None, Plot breaks curves at discontinuities and singularities it detects. Exclusions->None joins across discontinuities and singularities.
  • Exclusions->{x1,x2,…} is equivalent to Exclusions->{x==x1,x==x2,…}.
  • Possible settings for PlotLegends are:
  • Nonedo not include legends
    "Expressions"use a legend for the fi
    "ReIm"use a legend for the real and imaginary styles
    "ReImExpressions"use separate legends for the plot, real and imaginary styles
    Automaticuse a legend for all style combinations
    {lbl1,lbl2,…}use lbli to legend fi
    Placed[leg,pos]specify placement pos of legend leg
    {leg1,leg2,…}include multiple legends
  • PlotStyle determines the style for each function, and ReImStyle determines the style for the real and imaginary components.
  • Possible settings for ReImStyle include:
  • Automaticdefault styles
    {re,im}use re and im for the respective components
    {{re1,im1},{re2,im2},…}use different styles for different functions
  • ColorData["DefaultPlotColors"] gives the default sequence of colors used by PlotStyle.
  • Possible highlighting effects for Highlighted and PlotHighlighting include:
  • stylehighlight the indicated curve
    "Ball"highlight and label the indicated point in a curve
    "Dropline"highlight and label the indicated point in a curve with droplines to the axes
    "XSlice"highlight and label all points along a vertical slice
    "YSlice"highlight and label all points along a horizontal slice
    Placed[effect,pos]statically highlight the given position pos
  • Highlight position specifications pos include:
  • x, {x}effect at {x,y} with y chosen automatically
    {x,y}effect at {x,y}
    {pos1,pos2,…}multiple positions posi
  • ReImPlot initially evaluates f at a number of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to choose additional sample points, subdividing a given interval at most MaxRecursion times.
  • Since only a finite number of sample points are used, it is possible for ReImPlot to miss features of f. Increasing the settings for PlotPoints and MaxRecursion will often catch such features.
  • Themes that affect curves include:
  • "ThinLines"thin plot lines
    "MediumLines"medium plot lines
    "ThickLines"thick plot lines
  • The arguments supplied to functions in MeshFunctions and RegionFunction are x, y. Functions in ColorFunction are by default supplied with scaled versions of these arguments.
  • ScalingFunctions->"scale" scales the coordinate; ScalingFunctions{"scalex","scaley"} scales both the and coordinates.
  • List of all options

    • AlignmentPointCenterthe default point in the graphic to align with
      AspectRatio1/GoldenRatioratio of height to width
      AxesTruewhether to draw axes
      AxesLabelNoneaxes labels
      AxesOriginAutomaticwhere axes should cross
      AxesStyle{}style specifications for the axes
      BackgroundNonebackground color for the plot
      BaselinePositionAutomatichow to align with a surrounding text baseline
      BaseStyle{}base style specifications for the graphic
      ClippingStyleNonewhat to draw where curves are clipped
      ColorFunctionAutomatichow to determine the coloring of curves
      ColorFunctionScalingTruewhether to scale arguments to ColorFunction
      ContentSelectableAutomaticwhether to allow contents to be selected
      CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
      Epilog{}primitives rendered after the main plot
      EvaluationMonitorNoneexpression to evaluate at every function evaluation
      ExclusionsAutomaticpoints in x to exclude
      ExclusionsStyleNonewhat to draw at excluded points
      FillingNonefilling to insert under each curve
      FillingStyleAutomaticstyle to use for filling
      FormatTypeTraditionalFormthe default format type for text
      FrameFalsewhether to put a frame around the plot
      FrameLabelNoneframe labels
      FrameStyle{}style specifications for the frame
      FrameTicksAutomaticframe ticks
      FrameTicksStyle{}style specifications for frame ticks
      GridLinesNonegrid lines to draw
      GridLinesStyle{}style specifications for grid lines
      ImageMargins0.the margins to leave around the graphic
      ImagePaddingAllwhat extra padding to allow for labels etc.
      ImageSizeAutomaticthe absolute size at which to render the graphic
      LabelingSizeAutomaticmaximum size of callouts and labels
      LabelStyle{}style specifications for labels
      MaxRecursionAutomaticthe maximum number of recursive subdivisions allowed
      MeshNonehow many mesh points to draw on each curve
      MeshFunctions{#1&}how to determine the placement of mesh points
      MeshShadingNonehow to shade regions between mesh points
      MeshStyleAutomaticthe style for mesh points
      MethodAutomaticthe method to use for refining curves
      PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
      PlotHighlightingAutomatichighlighting effect for curves
      PlotLabelNoneoverall label for the plot
      PlotLabelsNonelabels to use for curves
      PlotLayoutAutomatichow to position curves
      PlotLegendsNonelegends for curves
      PlotPointsAutomaticinitial number of sample points
      PlotRange{Full,Automatic}the range of y or other values to include
      PlotRangeClippingTruewhether to clip at the plot range
      PlotRangePaddingAutomatichow much to pad the range of values
      PlotRegionAutomaticthe final display region to be filled
      PlotStyleAutomatichow to style individual functions fi
      PlotTheme$PlotThemeoverall theme for the plot
      PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
      Prolog{}primitives rendered before the main plot
      RegionFunction(True&)how to determine whether a point should be included
      ReImLabelsAutomatichow to annotate the real and imaginary components
      ReImStyleAutomatichow to style the real and imaginary components
      RotateLabelTruewhether to rotate y labels on the frame
      ScalingFunctionsNonehow to scale individual coordinates
      TargetUnitsAutomaticunits to display in the plot
      TicksAutomaticaxes ticks
      TicksStyle{}style specifications for axes ticks
      WorkingPrecisionMachinePrecisionthe precision used in internal computations

Examples

open all close all

Basic Examples  (3)

Plot the real and imaginary parts of a complex-valued function of a real variable:

Plot several functions:

Label each curve:

Scope  (23)

Sampling  (9)

More points are sampled where the function changes quickly:

The plot range is selected automatically:

Use PlotRange to focus in on areas of interest:

The curve is split when there are discontinuities in the function:

Use ExclusionsNone to draw connected curves:

Use PlotPoints and MaxRecursion to control adaptive sampling:

The domain can be specified by a region:

Specify a domain using a MeshRegion:

Plot over an infinite domain:

Labeling and Legending  (8)

There are two standard legends:

Show the legends together:

Use legends with combined styles:

Explicitly label the individual curves:

Identify curves with wrappers:

Curves usually have interactive callouts showing the coordinates when you mouse over them:

Choose from multiple interactive highlighting effects:

Use Highlighted to emphasize specific points in a plot:

Highlight multiple points:

Presentation  (6)

Multiple pairs of curves are automatically colored to be distinct:

Provide explicit styling to different curves:

Add labels and a legend:

Create filled plots:

Use a plot theme:

Use ScalingFunctions to scale the axes:

Options  (65)

ClippingStyle  (2)

Omit clipped regions of the plot:

Show clipped regions with red lines:

ColorFunction  (4)

Color by a scaled coordinate and scaled coordinate, respectively:

Use a named color gradient:

ColorFunction has higher priority than PlotStyle:

Highlight part of the plot:

ColorFunctionScaling  (1)

No argument scaling on the left; automatic scaling on the right:

Exclusions  (2)

In this case, the exclusion comes from a branch cut discontinuity:

Indicate that no exclusions should be computed:

ExclusionStyle  (1)

Use red lines to connect portions of the curve and black points to indicate exclusions:

Filling  (4)

Use symbolic or explicit values:

Fill between curve 1 and the axis:

Fill between curves 1 and 2:

Fill between the real and imaginary parts of each function:

FillingStyle  (3)

Use different fill colors:

Fill with red below the axis and blue above:

Use a variable filling style obtained from a ColorFunction:

MaxRecursion  (1)

Each level of MaxRecursion adaptively subdivides the initial mesh into a finer mesh:

Mesh  (3)

Show the initial and final sampling meshes:

Use 10 mesh points evenly spaced in the direction:

Use an explicit list of values for the mesh in the direction:

MeshFunctions  (2)

Use a mesh evenly spaced in the and directions:

Show seven mesh levels in the direction (red) and 15 in the direction (blue):

MeshShading  (3)

Alternate red and blue arcs in the direction:

MeshShading has higher priority than PlotStyle for styling:

Use PlotStyle for some segments by setting MeshShading to Automatic:

MeshStyle  (2)

Use a red mesh in the direction:

Use a red mesh in the direction and a blue mesh in the direction:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotHighlighting  (8)

Plots have interactive coordinate callouts with the default setting PlotHighlightingAutomatic:

Use PlotHighlightingNone to disable the highlighting for the entire plot:

Use Highlighted[…,None] to disable highlighting for a single curve:

Move the mouse over the curve to highlight it with a ball and label:

Use a ball and label to highlight a specific point on the curve:

Move the mouse over the curve to highlight it with a label and droplines to the axes:

Use a ball and label to highlight a specific point on the curve:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Highlight the curves at a fixed value:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Use a component that shows the points on the curve closest to the position of the mouse cursor:

Specify the style for the points:

Use a component that shows the coordinates on the curve closest to the mouse cursor:

Use Callout options to change the appearance of the label:

Combine components to create a custom effect:

PlotLabel  (1)

Add an overall label to the plot:

PlotLabels  (6)

Specify text to label curves:

Modify the appearance of the labels:

Place the labels differently for each curve:

PlotLabels"Expressions" uses functions as curve labels:

Use callouts to identify the curves:

Use None to not add a label:

PlotLegends  (7)

Create a legend based on the functions:

Use "ReIm" to distinguish between the real and imaginary parts of the function:

Use "ReImExpressions" to show both:

Use a legend showing all the style combinations:

Make two different legends:

Modify the legend labels:

Generate a third legend:

PlotPoints  (1)

Use more initial points to get smoother curves:

PlotRange  (1)

The plot range is selected automatically:

Focus on a specified range of values:

PlotStyle  (3)

Explicitly specify the style for different curves and regions:

ReImStyle takes precedence over PlotStyle:

Combine with ReImStyle:

PlotTheme  (3)

Use a theme with bright colors:

Add a theme with a legend:

Change plot styles:

RegionFunction  (1)

Show the curve where :

ReImLabels  (2)

Modify the labels for the real and imaginary parts of a function using predetermined option values:

Specify custom labels for the real and imaginary parts of a function:

ReImStyle  (2)

By default, the real and imaginary parts are solid and dashed, respectively:

Modify the real and imaginary styles:

Applications  (7)

Plot Fourier transforms:

Plot the solution of a complex differential equation with initial conditions:

Plot the eigenvalues of a matrix as a function of a parameter:

Plot solutions of an equation as a function of a parameter:

Graph special functions:

Plot fractional derivatives of :

Plot the complex solution of the Schrödinger equation for a particle in a box:

Properties & Relations  (8)

ReImPlot is a special case of Plot:

Use AbsArgPlot to plot the magnitude and argument over the real numbers:

ComplexPlot shows the argument and magnitude of a function using color:

Use ComplexPlot3D to use the z axis for the magnitude:

Use ComplexListPlot to show the location of complex numbers in the plane:

ComplexContourPlot plots curves over the complexes:

ComplexRegionPlot plots regions over the complexes:

ComplexStreamPlot and ComplexVectorPlot treat complex numbers as directions:

Possible Issues  (1)

ScalingFunctions applies to the real and imaginary parts:

See Also

AbsArgPlot  ComplexListPlot  ComplexPlot  ComplexPlot3D  ReIm  AbsArg  Plot  ParametricPlot

Related Guides

    ▪
  • Complex Visualization
  • ▪
  • Function Visualization
  • ▪
  • Functions of Complex Variables

History

Introduced in 2019 (12.0) | Updated in 2021 (13.0) ▪ 2023 (13.3)

Wolfram Research (2019), ReImPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ReImPlot.html (updated 2023).

Text

Wolfram Research (2019), ReImPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ReImPlot.html (updated 2023).

CMS

Wolfram Language. 2019. "ReImPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/ReImPlot.html.

APA

Wolfram Language. (2019). ReImPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ReImPlot.html

BibTeX

@misc{reference.wolfram_2025_reimplot, author="Wolfram Research", title="{ReImPlot}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/ReImPlot.html}", note=[Accessed: 01-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_reimplot, organization={Wolfram Research}, title={ReImPlot}, year={2023}, url={https://reference.wolfram.com/language/ref/ReImPlot.html}, note=[Accessed: 01-February-2026]}

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