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Re: complex numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105910] Re: [mg105904] complex numbers
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 24 Dec 2009 20:59:21 -0500 (EST)
  • Reply-to: hanlonr at cox.net

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.




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