MathGroup Archive 2009

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: complex numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105909] Re: [mg105904] complex numbers
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 24 Dec 2009 20:59:10 -0500 (EST)
  • Reply-to: hanlonr at cox.net

Presumably, because

Abs[x + I*y] // LeafCount

8

Sqrt[x^2 + y^2] // LeafCount

11


Bob Hanlon

---- Jon Joseph <josco.jon at gmail.com> wrote: 

=============
Thanks Bob. One question on you solutions: Since you declare both x and y to be real in the following


Assuming[{Element[{x, y}, Reals]},
#[{Re[z], Im[z], Abs[z]}] & /@ {Simplify, FullSimplify}]


Why doesn't Abs[z] expand to Sqrt[x^2+y^2] the same way it does in ComplexExpand?

Jon

On Dec 24, 2009, at 7:24 AM, Bob Hanlon wrote:

> 
> Clear[x, y, z];
> z = x + I*y;
> 
> {Re[z], Im[z], Abs[z]}
> 
> {Re[x] - Im[y], Im[x] + Re[y], Abs[x + I*y]}
> 
> Use assumptions to target specific variables as Real
> 
> Assuming[{Element[{x, y}, Reals]},
> #[{Re[z], Im[z], Abs[z]}] & /@ {Simplify, FullSimplify}]
> 
> {{x, y, Abs[x + I*y]}, {x, y, Abs[x + I*y]}}
> 
> Assuming[{Element[{x, y}, Reals]},
> #[{Re[z], Im[z], Abs[z]}] & /@ {Simplify, FullSimplify}]
> 
> {{x, y, Abs[x + I*y]}, {x, y, Abs[x + I*y]}}
> 
> If appropriate (i.e., all variables are Real), use ComplexExpand
> 
> {Re[z], Im[z], Abs[z]} // ComplexExpand
> 
> {x, y, Sqrt[x^2 + y^2]}
> 
> Use TagSet for x and y
> 
> x /: Im[x] = 0;
> x /: Re[x] = x;
> y /: Im[y] = 0;
> y /: Re[y] = y;
> 
> {Re[z], Im[z], Abs[z]}
> 
> {x, y, Abs[x + I*y]}
> 
> 
> Bob Hanlon
> 
> ---- Jon Joseph <josco.jon at gmail.com> wrote: 
> 
> =============
> All: Something fundamental about complex number initialization I am 
> failing to understand. I wish to define a complex number
> 
> 	z=x+ I y where x and y are both reals. Can someone tell me the 
> proper way to tell Mathematica that x, y are real so that Re[z] returns 
> x and Im[z] returns y? Much appreciated, Jon.
> 



  • Prev by Date: Re: complex numbers
  • Next by Date: Re: Function research
  • Previous by thread: Re: complex numbers
  • Next by thread: Re: complex numbers