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Re: Complex Numbers: Plotting Equations

• To: mathgroup at smc.vnet.net
• Subject: [mg37711] Re: [mg37684] Complex Numbers: Plotting Equations
• From: Vladimir Bondarenko <vvb at mail.strace.net>
• Date: Sat, 9 Nov 2002 00:29:32 -0500 (EST)
• In-reply-to: <200211080716.CAA07416@smc.vnet.net>
• References: <200211080716.CAA07416@smc.vnet.net>
• Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
• Sender: owner-wri-mathgroup at wolfram.com

kevin.stone at brainbashers.com (Kevin Stone) wrote on Friday, November 08, 2002, 3:16:00 AM :

KS> How do I go about plotting equations of the form:

KS> 1. |z-2i| = 6

Plot[Abs[z - 2I] - 6, {z, -3, 3}]

By the way, enjoy with a remarkable shape of

   Plot[Abs[z - 2I] - 6, {z, -100, 100}]

Can you explain it?


KS> 2. (2z-Conjugate(z))^2 = -6(z + Conjugate(z)

Plot[(2z - Conjugate[z])^2 + 6(z + Conjugate[z]), {z, -3, 3}]
Plot[(2z - Conjugate[z])^2 + 6(z + Conjugate[z]), {z, -30, 30}]
Plot[(2z - Conjugate[z])^2 + 6(z + Conjugate[z]), {z, -300, 300}]

KS> In addition, how can you solve the following in terms of exponentials?

KS> z^6 = 6 + 3i


Do you mean this?

Rationalize[N[Abs[6 + 3 I]Exp[I Arg[6 + 3 I]]]]

6 + 3 I

Solve[z^6 == Abs[6 + 3 I]Exp[I Arg[6 + 3 I]], z]

{{z -> -(3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2]))},
{{z -> {z -> 3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2])},
{z -> -((-1)^(1/3)*3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2]))},
{z -> {z -> (-1)^(1/3)*3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2])},
{z -> -((-1)^(2/3)*3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2]))},
{z -> {z -> (-1)^(2/3)*3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2])}}


Or something else?


Best wishes,

Vladimir Bondarenko

Email:  vvb at mail.strace.net

Web  :  http://www.CAS-testing.org/ (under development, 95% ready)
        http://maple.bug-list.org/  (under development, 20% ready)

• References:
  • Complex Numbers: Plotting Equations
    • From: kevin.stone@brainbashers.com (Kevin Stone)