H. Elbr\303\270nd Jensen, Matematisk Analyse 1, Kapitel 4Preben Alsholm, 25/1 2008restart;with(plots):libname:="g:/MatematikPakke/libDMat",libname;with(DMat);Eksempel 4.3(5+I)/(3-2*I);Eksempel 4.4c:=(-sqrt(3)+I)^10;evalc(%);c1:=-sqrt(3)+I;polar(c1);%^10;simplify(%,polar);evalc(%);Eksempel 4.5for k from 2 to 10 do cos(k*x)=expand(cos(k*x)) end do;for k from 2 to 10 do sin(k*x)=expand(sin(k*x)) end do;exp(I*v*n)=exp(I*v)^n;M:=map(convert,%,trig);for n from 2 to 6 do
res:=applyop(expand,2,M);
map(evalc@Re,res);
map(evalc@Im,res)
end do;Eksempel 4.6ligning:=z^2-(1+I)*z-2+2*I=0;solve(ligning,z);discrim(lhs(ligning),z);Eksempel 4.7ligning:=z^4=-8+8*I*sqrt(3);L:=solve(ligning,z);r:=abs(L[1]):
complexplot([L],style=point,symbol=solidcircle,symbolsize=20):
complexplot(r*exp(I*t),t=0..2*Pi,color=blue):
display(%%,%);polar(rhs(ligning));PolarForm(rhs(ligning));Eksempel 4.8P:=z^5+z^4+5*z^3+5*z^2+4*z+4;solve(P=0,z);factor(P);Eksempel 4.9P:=x^6+8;factor(P);solve(P=0,x);L:=evalc([%]);mul(x-L[k],k=1..6);L[1];Im(%);R\303\270dderne med positiv imagin\303\246rdel:Lp:=select(z->is(Im(z)>0),L);mul(expand( (x-Lp[k])*(x-conjugate(Lp[k])) ) ,k=1..3);Eksempel 4.10u:=cos(x)^2*sin(3*x);combine(u);Trin for trin:convert(u,exp);expand(%);combine(%);evalc(%);