# Plotting Complex Roots of Unity [duplicate]

Possible Duplicate:
Finding real roots of negative numbers (for example, $\sqrt$3${-8}$)

I am trying to make Mathematica plot the cube roots of $27i$ and graph them, so that I can include them in my $\LaTeX$ed homework. How can I do this?

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## marked as duplicate by R. M.♦, Verbeia♦, Oleksandr R., J. M.♦Sep 22 '12 at 2:43

From @belisarius

pts = ({Re@#, Im@#} & /@ (x /. Solve[x^3 == 27 I]))


Styling:

Show[ContourPlot[Abs[(x + I y)^3 - 27 I], {x, -4, 4}, {y, -4, 4}, Contours -> 15],
Graphics[{{Style[Text[#, #], 17] & /@ #}, {Opacity[.5], Orange,
Thickness[.01], Arrow[{{0, 0}, #}] & /@ #}, {Red,
PointSize[.02], Point@#}}, Axes -> True, Frame -> True,
PlotRangePadding -> 1, AspectRatio -> Automatic] &@pts]


Show[ContourPlot[Arg[(x + I y)^3 - 27 I], {x, -4, 4}, {y, -4, 4},
Contours -> 15, ColorFunction -> "Rainbow"],
Graphics[{{Style[Text[#, #], 17] & /@ #}, {Opacity[.5], Orange,
Thickness[.01], Arrow[{{0, 0}, #}] & /@ #}, {Red,
PointSize[.02], Point@#}}, Axes -> True, Frame -> True,
PlotRangePadding -> 1, AspectRatio -> Automatic] &@pts]


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