       Re: Solving complex equations

• To: mathgroup at smc.vnet.net
• Subject: [mg91204] Re: [mg91157] Solving complex equations
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 9 Aug 2008 07:46:33 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200808081112.HAA11483@smc.vnet.net>

```In such situations, ComplexExpand is your friend: it tells Mathematica
to treat symbolic variables as real, which I presume is your intent here.

So here's a start.  Obviously the process could be encapsulated into a
function.  I've used the infix @ notation for simplicity.

eq = a+b I+c+d I==3+4 I;

{ComplexExpand@Re@First@eq==ComplexExpand@Re@Last@eq,
ComplexExpand@Im@First@eq==ComplexExpand@Im@Last@eq}
{a+c==3,b+d==4}

> Dear all,
>
> If I have a complex equation in the form of
> a+b I + c+d I == 3+ 4 I
> where a, b, c, and d are all assumed to be real.
>
> How do I tell Mathematica 6 to separate the real and imaginary parts to make
> two equations in the form of
> a + c == 3, and
> b + d == 4.
>
> I need this to apply it on a long list of equations.
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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