Komplexné čísla

z=1+Sqrt[3]I

Re[z]

Im[z]

Sqrt[Re[z]^2+Im[z]^2]

Abs[z]

a=Plot[Im[z]/Re[z]  x,{x,0,1},AspectRatio->Automatic,DisplayFunction->Identity];
b=Graphics[{AbsolutePointSize[10],RGBColor[1,0,0],Point[{Re[z],Im[z]}]}];
Show[a,b,DisplayFunction->$DisplayFunction]

ArcTan[Im[z]/Re[z]]

(%/Degree)//N

Arg[z]

w=Conjugate[z]

Abs[w]

Arg[w]

Show[Graphics[{{AbsolutePointSize[10],RGBColor[1,0,0],Point[{Re[z],Im[z]}]},
{AbsolutePointSize[10],RGBColor[0,1,0],Point[{Re[w],Im[w]}]},
{RGBColor[0,0,1],Circle[{0,0},Abs[z]]}}]]

Show[Graphics[{{AbsolutePointSize[10],RGBColor[1,0,0],Point[{Re[z],Im[z]}]},
{AbsolutePointSize[10],RGBColor[0,1,0],Point[{Re[w],Im[w]}]},
{RGBColor[0,0,1],Circle[{0,0},Abs[z]]},
Line[{{-Abs[z]-1,0},{Abs[z]+1,0}}],
Line[{{0,-Abs[z]-1},{0,Abs[z]+1}}]}]]

r=Solve[x^3==1,x]

c=x/.r//N

Abs[c[[1]]]

Abs[c[[3]]]

{x,y,z}=x/.r//N

z

Show[Graphics[{{AbsolutePointSize[10],RGBColor[1,0,0],Point[{Re[x],Im[x]}]},
{AbsolutePointSize[10],RGBColor[0,1,0],Point[{Re[y],Im[y]}]},
{AbsolutePointSize[10],RGBColor[0,0,1],Point[{Re[z],Im[z]}]},
{RGBColor[0,0,1],Circle[{0,0},Abs[z]]},
Line[{{-Abs[z]-1,0},{Abs[z]+1,0}}],
Line[{{0,-Abs[z]-1},{0,Abs[z]+1}}]}]]