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

• To: mathgroup at smc.vnet.net
• Subject: [mg121186] Re: Output complex numbers in polar (exponential) form?
• From: Simon <simonjtyler at gmail.com>
• Date: Sat, 3 Sep 2011 08:04:52 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j3q0pm$6fh$1@smc.vnet.net>
• Reply-to: comp.soft-sys.math.mathematica at googlegroups.com

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.