Wolfram Language

Algebra and Number Theory

Representations of Complex Numbers

The new functions ReIm and AbsArg make it easy to convert a complex number to either its Cartesian or polar representation.

Convert a complex number to the ordered pair .

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ReIm[3 + 4 I]
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Convert several numbers.

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ReIm[{Pi, -2 I, Sqrt[-I], 3 Exp[I 2 Pi/3]}]
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Convert a complex number to the ordered pair .

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AbsArg[3 + 4 I]
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Convert several numbers.

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AbsArg[{Pi, -2 I, Sqrt[-I], 3 Exp[I 2 Pi/3]}]
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Plot a complex-valued function as a curve in the complex plane.

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ParametricPlot[ReIm[(-2)^x], {x, 0, 4}]
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Annotate specific points in a complex-plane plot.

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JuliaSetPlot[-1, PlotRange -> 1.75, Epilog -> {PointSize[Large], White, Point[ReIm[{I/2, -I/2, 1, -1}]]}]
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