ComplexListPlot

ComplexListPlot[{z1,z2,}]

plots complex numbers z1, z2, as points in the complex plane.

ComplexListPlot[{data1,data2,}]

plots data from all datai.

ComplexListPlot[{,w[datai,],}]

plots data_(i) with features defined by the symbolic wrapper w.

Details and Options

Examples

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Basic Examples  (4)

Plot a set of complex numbers:

Plot multiple sets of complex numbers:

Plot several data_i with a legend:

Label each point with a callout:

Scope  (38)

Data  (7)

A list of complex values is plotted as a list of {Re[z_(i)],Im[z_(i)]} pairs:

Plot multiple sets of regular data:

Non-numeric and missing data is excluded:

Use MaxPlotPoints to limit the number of points used:

PlotRange is selected automatically:

Use PlotRange to focus on areas of interest:

Use ScalingFunctions to scale the axes:

Special Data  (4)

Specify strings to use as labels:

Specify a location for labels:

Numeric values in an Association are used as the (x,y) coordinates:

Plot data in a SparseArray:

Wrappers  (6)

Use wrappers on individual data, datasets or collections of datasets:

Wrappers can be nested:

Use a specific label for all of the points:

Label points with automatically positioned text:

Use PopupWindow to click an eigenvalue to see a corresponding eigenvector:

Button can be used to trigger any action:

Labeling and Legending  (15)

Label points with automatically positioned text:

Place the labels relative to the points:

Label data with Labeled:

Label data with PlotLabels:

Place the label near the points at a particular x value:

Use a scaled position:

Specify the text position relative to the point:

Label data automatically with Callout:

Place a label with a specific location:

Specify label names with LabelingFunction:

For dense sets of points, some labels may be turned into tooltips by default:

Increasing the size of the plot will show more labels:

Include legends for each datai:

Use Legended to provide a legend for a specific dataset:

Use Placed to change the legend location:

Use association keys as labels:

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

Presentation  (6)

Multiple datasets are automatically colored to be distinct:

Provide explicit styling to different sets:

Use a plot theme:

Include legends for each dataset:

Use Legended to provide a legend for a specific dataset:

Provide an interactive Tooltip for the data:

Use shapes to distinguish different datasets:

Use labels to distinguish different datasets:

Use Joined to connect datasets with lines:

Use InterpolationOrder to smooth joined data:

Options  (156)

AspectRatio  (4)

By default, the ratio of the height to width for the plot is determined automatically:

Use numerical value to specify the height to width ratio:

Make the height the same as the width with AspectRatio1:

AspectRatioFull adjusts the height and width to tightly fit inside other constructs:

Axes  (3)

By default, ComplexListPlot draws axes:

Use AxesOrigin to specify where the axes intersect:

Turn each axis on individually:

AxesLabel  (3)

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

AxesOrigin  (2)

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

AxesStyle  (4)

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

ClippingStyle  (4)

ClippingStyle requires at least one dataset to be Joined:

Omit clipped regions of the plot:

Show clipped regions as red at the bottom and thick at the top:

Show clipped regions as red and thick:

ColorFunction  (3)

Color by scaled x, y, theta and r coordinates:

ColorFunction has higher priority than PlotStyle for coloring the curve:

Use Automatic in MeshShading to use ColorFunction:

ColorFunctionScaling  (4)

ColorFunctionScaling requires at least one dataset to be Joined:

Color the curve based on the scaled y value:

Color the curve based on the unscaled y value:

Color by unscaled x, y, theta and r coordinates:

Frame  (3)

Draw a frame around the plot:

Draw a frame on the left and right edges:

Draw a frame on the left and bottom edges:

FrameLabel  (4)

Place a label along the bottom edge of the frame:

Place labels on the bottom and left edges:

Place labels on each of the edges in the frame:

Use a customized style for both labels and frame tick labels:

FrameStyle  (2)

Specify a style for the frame:

Specify a style for each frame edge:

FrameTicks  (9)

Frame ticks are placed automatically by default:

Use a frame with no ticks:

Use frame ticks on the bottom edge:

By default, the top and right edges have tick marks but no tick labels:

Use All to include tick labels on all edges:

Place tick marks at specific positions:

Draw frame tick marks at specified positions with specific labels:

Specify the lengths for tick marks as a fraction of the graphics size:

Use different sizes in the positive and negative directions for each tick mark:

Specify a style for each frame tick:

Construct a function that places frame ticks at the midpoint and extremes of the frame edge:

FrameTicksStyle  (3)

By default, frame ticks and frame tick labels use the same styles as the frame:

Specify an overall style for the ticks, including the labels:

Use different styles for the different frame edges:

ImageSize  (8)

Use named sizes such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull to fill the available space in an object:

Specify the image size as a fraction of the available space:

The number of points that are labeled directly may depend on the image size:

Smaller graphics will have fewer labeled points:

Larger graphics will have more labeled points:

InterpolationOrder  (4)

InterpolationOrder requires at least one dataset to be Joined:

By default, linear interpolation is used:

Use zero-order or piecewise-constant interpolation:

Interpolation order 0 to 3:

Joined  (3)

Join the points in a dataset:

Join the first dataset with a line, but use points for the second dataset:

Join the dataset with a line and show the original points:

LabelingFunction  (7)

A Rule can be used to label points if the lists of values and labels are the same length:

A list of rules and values can be used to label selected points:

Use LabelingFunctionNone to suppress the labels:

Put the labels above the points:

Put them in a Tooltip:

Label the points as ordered pairs:

Label the points with their indices:

LabelingSize  (3)

Textual labels are shown at their actual sizes:

Specify a maximum size for textual labels:

Image labels are automatically resized:

Specify a maximum size for image labels:

Show image labels at their natural sizes:

MaxPlotPoints  (1)

Use MaxPlotPoints to limit the number of points used:

Mesh  (6)

Mesh requires at least one dataset to be Joined:

The initial and final sampling meshes are typically the same:

Interpolated data may introduce points:

Use 20 mesh levels evenly spaced in the direction:

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

Use explicit styles at specific points:

MeshFunctions  (3)

MeshFunctions requires at least one dataset to be Joined:

Show 5 mesh levels in the direction (red) and 10 in the direction (blue):

Use a mesh evenly spaced in the , , and directions:

MeshShading  (7)

MeshShading requires at least one dataset to be Joined:

Alternate red and blue segments of equal width in the direction:

Use None to remove segments:

MeshShading can be used with PlotStyle:

MeshShading has higher priority than PlotStyle:

Use PlotStyle for some segments by setting MeshShading to Automatic:

MeshShading can be used with ColorFunction:

PlotHighlighting  (7)

Plots have interactive coordinate callouts with the default setting PlotHighlightingAutomatic:

Use PlotHighlightingNone to disable the highlighting for the entire plot:

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

Move the mouse over a set of points to highlight it using arbitrary graphics directives:

Move the mouse over the points to highlight them with balls and labels:

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

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

Specify the style for the points:

Use a component that shows the coordinates on the points 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  (5)

Specify text to label sets of points:

Place the labels above the points:

Use callouts to identify the points:

Use the keys from an Association as labels:

Use None to not add a label:

PlotLegends  (6)

Generate a legend using labels:

Generate a legend using placeholders:

Legends use the same styles as the plot:

Use Placed to specify the legend placement:

Place the legend inside the plot:

Use PlotLegends to change the appearance:

PlotMarkers  (8)

ComplexListPlot normally uses distinct colors to distinguish different sets of data:

Automatically use colors and shapes to distinguish sets of data:

Use shapes only:

Change the size of the default plot markers:

Use arbitrary text for plot markers:

Use explicit graphics for plot markers:

Use the same symbol for all the sets of data:

Explicitly use a symbol and size:

PlotRange  (4)

PlotRange is automatically calculated:

Show the whole dataset:

Explicitly choose the x and y ranges:

Implicitly choose the x and y ranges by giving complex coordinates of the bottom-left and top-right corners:

PlotStyle  (7)

Use different style directives:

By default, different styles are chosen for multiple datasets:

Explicitly specify the style for different datasets:

PlotStyle applies to both curves and points:

PlotStyle can be combined with ColorFunction:

PlotStyle can be combined with MeshShading:

MeshStyle by default uses the same style as PlotStyle:

PlotTheme  (2)

Use a theme with simple ticks and grid lines in a bright color scheme:

Change the color scheme:

PolarAxes  (2)

Add polar axes and polar grid lines:

Control the radial and polar axes independently:

PolarAxesOrigin  (2)

Specify the angular axes and radial axes to intersect at :

Place radial axes at the right of the graph:

PolarGridLines  (2)

Use automatically chosen polar grid lines:

Draw grid lines at the specified positions:

PolarTicks  (4)

Place polar tick marks and labels automatically:

Modify the angular ticks:

Indicate angles with degrees:

Place polar tick marks at the specified positions:

ScalingFunctions  (3)

A single scaling function scales the data radially:

Specifying two scaling functions scales the data in the x and y directions separately:

None indicates no scaling in the specified direction:

Ticks  (9)

Ticks are placed automatically for each axis:

Use TicksNone to draw axes without any tick marks:

Use ticks on the axis, but not the imaginary axis:

Place tick marks at specific positions:

Draw tick marks at the specified positions with specific labels:

Use specific ticks on one axis and automatic ticks on the other:

Specify the lengths for ticks as a fraction of graphics size:

Use different sizes in the positive and negative directions for each tick:

Specify a style for each tick:

Construct a function that places ticks at the midpoint and extremes of the axis:

TicksStyle  (4)

By default, the ticks and tick labels use the same styles as the axis:

Specify an overall ticks style, including the tick labels:

Specify ticks style for each of the axes:

Use a different style for the tick labels and tick marks:

Applications  (9)

Plot roots of unity:

Plot a discrete time signal and its spectrum:

Graph zeros of the zeta function:

Graph eigenvalues of a Cauchy matrix:

Graphs solutions of :

Show Gershgorin discs and eigenvalues for a matrix:

Show the eigenvalues for a PDE problem. Seek solutions of the structurally damped wave equation , of the form :

Visualize iterations of Newton's method:

The eigenvalues of bipartite graphs are symmetric about the imaginary axis:

Properties & Relations  (9)

Use ListPlot, ListLinePlot or ListPolarPlot for real data:

ComplexListPlot is closely related to ListPlot:

Use ComplexPlot to use color to show the argument and magnitude of a function:

Use ComplexPlot3D to use the axis for the magnitude:

Use ComplexArrayPlot for arrays of complex numbers:

Use ReImPlot and AbsArgPlot to plot complex values over the real numbers:

ComplexContourPlot plots curves over the complexes:

ComplexRegionPlot plots regions over the complexes:

ComplexStreamPlot and ComplexVectorPlot treat complex numbers as directions:

Possible Issues  (2)

Real-valued data is plotted along the axis.:

Radial scaling is different when using the same scaling functions in the real and imaginary directions:

Neat Examples  (3)

Eigenvalue analysis of the weighted adjacency matrix of the wins by teams in the National Hockey League in the 20102011 regular season:

Symmetry in the real parts of the eigenvalues of an adjacency matrix for a graph suggests that the graph may be bipartite, but in this case the graph is not bipartite:

Compute an integer two times the numbers in {0,1,,n-1} modulo :

Graphically represent the integer as the point in the complex plane and connect the dots between the points representing and TemplateBox[{{m,  , x}, n}, Mod]:

If you use a larger value of , then an envelope appears:

Use multiples of three and five instead:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2023_complexlistplot, author="Wolfram Research", title="{ComplexListPlot}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexListPlot.html}", note=[Accessed: 13-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_complexlistplot, organization={Wolfram Research}, title={ComplexListPlot}, year={2023}, url={https://reference.wolfram.com/language/ref/ComplexListPlot.html}, note=[Accessed: 13-April-2024 ]}