Root

Author

Eric W. Weisstein
April 15, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/Root.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Root.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Example

eqn=z^3-z^2-z-1;
{re,im}=ComplexExpand[Through[{Re,Im}[Expand[eqn/.z->x+I y]]]]

roots=z/.{ToRules[Roots[z^3-z^2-z-1==0,z,Cubics->False]]}

roots//N

Plot

<<Graphics`ImplicitPlot`
<<Graphics`Colors`
<<Typesetting`

ImplicitPlot[{
re==0,
im==0
},{x,-4.5,4},PlotStyle->{Red,Blue,Green},
Epilog->{PointSize[.03],Point[Through[{Re,Im}[#]]]&/@roots},
PlotPoints->150,AspectRatio->Automatic,PlotRange->{{-1,1},{-1,1}}3,
AxesLabel->TraditionalForm/@{x,y},
PlotLabel->TraditionalForm[eqn==0]
]