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