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Re: Output complex numbers in polar (exponential) form?

• To: mathgroup at smc.vnet.net
• Subject: [mg121298] Re: Output complex numbers in polar (exponential) form?
• From: "Mr.CRC" <crobcBOGUS at REMOVETHISsbcglobal.net>
• Date: Thu, 8 Sep 2011 05:25:59 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j3q0pm$6fh$1@smc.vnet.net> <j3t5bg$57f$1@smc.vnet.net>

Simon wrote:
> Here's the answer I gave to a similar question (http://stackoverflow.com/q/3928489/421225) on stackoverflow.
> 
> If you only need to do it occasionally, then you could just define a function like
> 
> ComplexToPolar[z_] /; Element[z, Complexes] := 
>  Interpretation[
>   Grid[{{Abs[z], Superscript[E, Row[{I, Arg[z]}]]}}, Spacings -> .2], 
>   z]
> 
> If always want objects with Head Complex, then something like
> 
> Unprotect[Complex];
> Complex /: MakeBoxes[Complex[a_, b_], StandardForm] := 
>  With[{abs = Abs[Complex[a, b]], arg = Arg[Complex[a, b]]}, 
>   RowBox[{MakeBoxes[abs, StandardForm], 
>     SuperscriptBox["\[ExponentialE]", 
>      RowBox[{"\[ImaginaryI]", MakeBoxes[arg, StandardForm]}]]}]]
> Protect[Complex];
> 
> For complex numbers such as 3 + 4 Pi I, the first option works, but the second doesn't. This is clear from the FullForm.
> 


Thanks for the response.

I think the first option works.


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Mr.CRC
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