RE: Complex Numbers: Plotting Equations
- To: mathgroup at smc.vnet.net
- Subject: [mg37691] RE: [mg37684] Complex Numbers: Plotting Equations
- From: "Florian Jaccard" <jaccardf at eicn.ch>
- Date: Sat, 9 Nov 2002 00:28:39 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello Kevin ! 1) In[1]:= << "Algebra`ReIm`" In[2]:= x /: Im[x] = 0; y /: Im[y] = 0; z = x + I*y; In[7]:= << "Graphics`ImplicitPlot`" In[11]:= ImplicitPlot[ComplexExpand[Abs[z - 2*I], TargetFunctions -> {Re, Im}] == 6, {x, -7, 7}]; 2) Could be done in the same way, but is not interesting. In fact, In[16]:= ComplexExpand[(2*z - Conjugate[z])^2, TargetFunctions -> {Re, Im}] Out[16]= x^2 + 6*I*x*y - 9*y^2 In[17]:= ComplexExpand[-6*(z + Conjugate[z]), TargetFunctions -> {Re, Im}] Out[17]= -12*x So x*y = 0 and x^2-9y^2=12*x. The only point is (0;0) ! 3) The best is to do it "by hand" : Table[Print["solution ", i, " : z = ", Abs[6 + 3*I]^(1/6), Simplify[ E^((Arg[6 + 3*I]/6)*I + i*2*(Pi/6))]], {i, 0, 5}]; Meilleures salutations Florian Jaccard -----Message d'origine----- De : Kevin Stone [mailto:kevin.stone at brainbashers.com] Envoyé : ven., 8. novembre 2002 08:16 À : mathgroup at smc.vnet.net Objet : [mg37684] Complex Numbers: Plotting Equations Hi, How do I go about plotting equations of the form: 1. |z-2i| = 6 2. (2z-Conjugate(z))^2 = -6(z + Conjugate(z) In addition, how can you solve the following in terms of exponentials? z^6 = 6 + 3i Thanks. Kev