       Re: Complex numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg37141] Re: [mg37138] Complex numbers
• From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
• Date: Sun, 13 Oct 2002 05:56:21 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```To start with, what you are saying is simply not true. A simple example:

In:=
Abs[(z1 - z2)/(1 - z1*Conjugate[z2])] /.
{z1 -> 1 + I, z2 -> 1 - I}

Out=
2/Sqrt

Presumably you meant Abs[(z1 - z2)/(z1 - Conjugate[z2]) in which case:

In:=
ComplexExpand[Abs[(z1-z2)/(z1- Conjugate[z2])],TargetFunctions->{Im,Re}]

Out=
1

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/

On Saturday, October 12, 2002, at 06:05 PM, CeZaR wrote:

> Hi,
>
> I want to perform this calculation:
>
> In:=z1 = a1 + b1 I
> Out=a1 + \[ImaginaryI] b1
> In:=z2 = a2 + b2 I
> Out=a2 + \[ImaginaryI] b2
> In:=Abs[(z1 - z2)/(1 - z1 Conjugate[z2])]
>
> This should output 1! But it doesn't work...
>
> Also, Abs[a1+b1 I] doesn't get the right result.
> Any ideeas?
>
> Thanks,
> CeZaR
>
>
>

```

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