(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 10443, 265]*) (*NotebookOutlinePosition[ 11498, 301]*) (* CellTagsIndexPosition[ 11454, 297]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[ "\nOff[General::spell];\nOff[General::spell1];\nOff[Plot::plnr];\n\ Off[ParametricPlot::ppcom];\nNeeds[\"Graphics`Colors`\"]\n\ Needs[\"Miscellaneous`Units`\"]\nNeeds[\"Algebra`Trigonometry`\"]\n\ Clear[Derivative]\nThreeAxes[u,v]\n\n\nThreeAxes[u_,v_] := \n \ Graphics3D[{\n {Blue,Line[{{-u,0,0},{u,0,0}}]},\n \ Text[\"x\",{u + v,0,0}],\n {Blue,Line[{{0,-u,0},{0,u,0}}]},\n \ Text[\"y\",{0, u + v,0}],\n \ {Blue,Line[{{0,0,0},{0,0,u}}]},\n Text[\"z\",{0,0,u + \ v}]}]; \nThreeAxes[u_] := ThreeAxes[u,u/8];\nThreeAxes::usage = \ \"ThreeAxes[a,b] makes a standard cartesian axis graphics object\n\twith x, \ y, and z running from -a to a, and with axis\n\tlabels b units beyond the \ tips of the axes. 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This notebook shows graphically that when two complex numbers are \ multiplied, their arguments are added.", Evaluatable->False, PageBreakBelow->Automatic, AspectRatioFixed->True, FontSize->12] }], "Subsection", Evaluatable->False, PageBreakBelow->Automatic, AspectRatioFixed->True, FontSize->14], Cell[TextData[StyleBox[ "\nGiven two complex numbers z1 and z2, the first two 'do loops' display \ their arguments as adjacent sectors of a circle whose angles are the \ arguments of the numbers, with z1 in orange and z2 in light blue. The union \ of these two sectors forms a larger sector whose angle is the sum of the \ arguments of z1 and z2. \n \nThe third and last 'do loop' displays the \ adjacent sectors representing the arguments of z1 and z2 and has a third \ violet sector representing the argument of z3 = z1*z2. 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