Re: Complex and Solve

• To: mathgroup at smc.vnet.net
• Subject: [mg125143] Re: Complex and Solve
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 24 Feb 2012 00:57:56 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201202211115.GAA08330@smc.vnet.net>

```Actually I should have checked, with version 8 Solve can handle
inequalities so either Reduce or Solve works here.

\$Assumptions = rfe > 0 && l > 0;

r = 1;
\[Omega] = 300;
vrms = 2;
irms = 1/2;
\[Phi] = 30 Degree;

impedance = r + 1/(1/rfe + 1/(I \[Omega] l)) // FullSimplify;

voltage = vrms (Cos[\[Phi]] + I Sin[\[Phi]]) // Simplify;

Solve[{irms == voltage/impedance, \$Assumptions}, {rfe,
l}][[1]] // FullSimplify

{rfe -> (1/11)*(-7 + 30*Sqrt[3]), l -> (1/600)*(17 - 4*Sqrt[3])}

Alternatively,

Solve[{irms == voltage/impedance, Im[l] == 0, Im[rfe] == 0}, {rfe,
l}][[1]] // FullSimplify

{rfe -> (1/11)*(-7 + 30*Sqrt[3]), l -> (1/600)*(17 - 4*Sqrt[3])}

Bob Hanlon

On Thu, Feb 23, 2012 at 5:46 AM,  <howard.lovatt at gmail.com> wrote:
> Thanks Bob,
>
> Your solution is much better than mine. I had no idea that Reduce could be used like you showed.
>
> Bizarre that Solve and Reduce behave so differently!
>
> Thanks again,
>
>  -- Howard.
>

--
Bob Hanlon

```

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