Re: Is this a bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg90861] Re: Is this a bug?
• From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
• Date: Sat, 26 Jul 2008 04:23:59 -0400 (EDT)
• References: <g6c982\$brv\$1@smc.vnet.net>

```"mailcwc at gmail.com" <mailcwc at gmail.com> wrote:
> I tried to solve the following equation with mathematica 6.03
>
> Solve[{Abs[X+Y I]==5,X==3},{X,Y}]
>
>
> {{X -> 3, Y -> -2 I}, {X -> 3, Y -> 8 I}}

It's easy to verify that both of those solutions are correct.

> Am I  suppose to get {{X -> 3, Y -> 4 I}, {X -> 3, Y -> -4 I}} ?

No. Rather, I think that you were wanting Y itself to be real, and so you
should have been hoping for

{{X -> 3, Y -> 4}, {X -> 3, Y -> -4}}

In any event, it seems that you were wanting Mathematica to find the
possible imaginary parts of complex numbers having real part 3 and
modulus 5. The way I'd do that is

In[1]:= Reduce[Abs[3 + Im[z]*I] == 5, z]

Out[1]= Im[z] == -4 || Im[z] == 4

the two solutions which your Solve gave are correct. But I think that
Mathematica is perhaps at fault for not having warned you that Solve was
not necessarily giving you all possible solutions.

David

```

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