Komplexe Zahlen

I

I

z=x+I y

?Re

ComplexExpand[Re[z]]

ComplexExpand[Im[z]]

(1/z)

ComplexExpand[(1/z)]

Abs[z]

ComplexExpand[Abs[z]]

Conjugate[z]

Solve[ComplexExpand[Im[((z-2)/(z-I))]]==0,{x,y}]

Solve[ComplexExpand[Abs[((z+2)/(z-I))]]==2,{x,y}]

Arg[-1+I]

ArcCos[((-1)/(Sqrt[2]))]

Arg1[ϕ_]:=2 ArcTan[((Sin[ϕ])/(1+Cos[ϕ]))]

Plot[Arg1[ϕ],{ϕ,-π,π},AspectRatio->Automatic]

ComplexExpand[Exp[I x]]

Umrechnen der Zahldarstellungen

z=3-3 (Sqrt[3]) I

{Abs[z],2ArcTan[((Im[z])/(Abs[z]+Re[z]))],Arg[z]}//FullSimplify

ComplexExpand[6 (E^((-I π)/3))]

ComplexExpand[(Sqrt[2]) (E^((I π)/4))]

Cardanische Formeln

Plot[(x^2)-3x-1,{x,-4,4}]

Solve[(x^2)-3x-1==0,x]

Plot[(x^3)-3x-1,{x,-4,4}]

sol=Solve[(x^3)-3x-1==0,x]

N[sol]

Plot[(x^4)-3x-1,{x,-3,3}]

sol=Solve[(x^4)-3x-1==0,x]

N[sol]

Multiplikation

z=1+I

w=-1+I

(z^5)(w^7)

(z^5)

(w^7)

Clear[z]

Solve[(z^5)==1,z]

sol=Solve[(z^5)==1,z]//ComplexExpand