({{Číslo projektu, CZ.1.07/1.1.36/02.0066}, {Autor, Karel Johanovský}, {Téma, Příkaz Manipulate 3}, {Metodický pokyn, výkladový text pro učitele inovátory}})

Příkaz Manipulate 3

Argandův diagram

staženo z : http : // demonstrations.wolfram.com/data/000201/0029/ArgandDiagram/ArgandDiagram - source.nb

Manipulate[LocatorPane[pt={r Cos[θ],r Sin[θ]};Dynamic[pt,(r=Norm[#];If[r==0,r=.0001];θ=If[#[[2]]>=0,ArcCos[#[[1]]/r],2Pi-ArcCos[#[[1]]/r]];)&],Dynamic@Graphics[
{
Circle[],
{
RGBColor[.24,.39,.77],
Line[r{{0,0},{Cos[θ],0},{Cos[θ],Sin[θ]},{0,0}}],
RGBColor[1,.47,0],
Dashing[{.02}],Circle[{0,0},r]
},
Arrow[{{0,-1},{0,1}}],
Arrow[{{-1,0},{1,0}}],
Text[Style["x",Italic,14],{1.1,0}],
Text[Style["y",Italic,14],{0,1.1}],
Text[Style[TraditionalForm[PaddedForm[Chop[r(Cos[θ]+I Sin[θ])],{4,3}]],14],(r+If[Mod[θ,2π]==0.,.25,.37+.15Cos[2θ]]){Cos[θ],Sin[θ]},{0,0},Background->White]},
ImageSize->{500,400},ImagePadding->{{90,90},{60,60}},PlotRange->{2{-1,1},2{-1,1}}],Appearance->Graphics[{PointSize[.03],RGBColor[1,.47,0],Point[{0,0}]}]],{{pt,{.5,.5}},{-1,-1},{1,1},ControlType->None},{{θ,π/4.,"argument"},0.,2π,Appearance->"Labeled"},{{r,.5,"modulus"},0.,Norm[{2,2}],Appearance->"Labeled"}]

Komplexní číslo

staženo z : http : // demonstrations.wolfram.com/data/004336/0011/ComplexNumber/ComplexNumber - source.nb

Manipulate[
r=Norm[xy];
If[r==0,r=.1];
If[showAngle,θ=Arg[xy[[1]]+xy[[2]] I],θ=If[Arg[xy[[1]]+xy[[2]] I]≥0,Arg[xy[[1]]+xy[[2]] I],Arg[xy[[1]]+xy[[2]] I]+2 π]];Graphics[{{White,Rectangle[{-6,6},{6,8}]},{Lighter[Yellow,0.85],Rectangle[{-6,-6},{6,6}]},{Lighter[Black,0.5],Opacity[0.5],AbsoluteThickness[1],Arrow[{{0,-5},{0,5}}],Arrow[{{-5,0},{5,0}}]},{RGBColor[.6,.73,.36],Opacity[1],AbsoluteThickness[2],Line[{{0,0},xy}]},{RGBColor[.25,.43,.82],Opacity[1],AbsoluteThickness[2],Line[{{xy[[1]],0},xy}]},{RGBColor[.49,0,0],Opacity[1],AbsoluteThickness[2],Line[{{0,xy[[2]]},xy}]},{Black,Opacity[1],AbsolutePointSize[5],Point[xy]},{RGBColor[.6,.73,.36],Opacity[0.2],Disk[{0,0},r,If[showAngle&&θ<0,{θ,0},{0,θ}]]},{Opacity[0.7],If[showGon,Text[Style[TraditionalForm[ToString[PaddedForm[N@Abs[xy[[1]]+I xy[[2]]],{4,3}]]*Power[e,ToString[PaddedForm[N@θ,{4,3}]]<>ToString["I"]]],RGBColor[.25,.43,.82],14],xy,If[0≤θ≤π,{0,-1},{0,1}]],Text[Style[TraditionalForm[PaddedForm[Chop[N@xy[[1]]+I xy[[2]]],{4,3}]],Black,14],xy,If[0≤θ≤π,{0,-1},{0,1}]]]},{Opacity[0.7],Text[Style[Row[{"Re(",Style["z",Italic],") = ",ToString[PaddedForm[N@Chop[Re[xy[[1]]+I xy[[2]]]],{4,3}]]}],RGBColor[.49,0,0],12],{-5.5,7.4},{-1,0}]},{Opacity[0.7],Text[Style[Row[{"Im(",Style["z",Italic],") = ",ToString[PaddedForm[N@Chop[Im[xy[[1]]+I xy[[2]]]],{4,3}]]}],RGBColor[.25,.43,.82],12],{-5.5,6.6},{-1,0}]},
{
Text[Style[Row[{"abs(",Style["z",Italic],") = ",ToString[PaddedForm[N@Chop[Abs[xy[[1]]+I xy[[2]]]],{4,3}]]}],RGBColor[.6,.73,.36],12],{2,7.4},{-1,0}]},
{
Text[Style[Row[{"arg(",Style["z",Italic],") = ",ToString[PaddedForm[N@Chop[θ],{4,3}]]}],RGBColor[.6,.73,.36],12],{2,6.6},{-1,0}]}
},PlotRange->{{-6,6},{-6,8}},AspectRatio->1,ImageSize->450],{{showAngle,True,"argument (phase) from (-π,π]"},{True,False}},{{showGon,False,"phasor form"},{True,False}},
{{xy,{-2.001,-2.501}},{-4,-4},{4,4},ControlType->Locator,Appearance->Style["●",12,RGBColor[.6,.73,.36]]},
TrackedSymbols->Manipulate]