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Re: Re: Trigonometric form of complex numbers
*To*: mathgroup at smc.vnet.net
*Subject*: [mg64199] Re: [mg64181] Re: Trigonometric form of complex numbers
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Sun, 5 Feb 2006 04:44:53 -0500 (EST)
*Reply-to*: hanlonr at cox.net
*Sender*: owner-wri-mathgroup at wolfram.com
p[x_]:=Abs[x]*(Cos[Arg[x]]+I*Sin[Arg[x]]);
f[y_,n_Integer]:=Module[{x},
p/@(x/.Solve[x^n==y,x])];
r=f[z,3]
{Abs[z]^(1/3)*(Cos[Arg[z]/3] + I*Sin[Arg[z]/3]),
Abs[z]^(1/3)*(Cos[Arg[(-(-1)^(1/3))*z^(1/3)]] +
I*Sin[Arg[(-(-1)^(1/3))*z^(1/3)]]),
Abs[z]^(1/3)*(Cos[Arg[(-1)^(2/3)*z^(1/3)]] +
I*Sin[Arg[(-1)^(2/3)*z^(1/3)]])}
FullSimplify[Times@@r]
z
However, you can get the sign inverted
r=f[5+I*6,2]
{61^(1/4)*(Cos[Arg[-Sqrt[5 + 6*I]]] +
I*Sin[Arg[-Sqrt[5 + 6*I]]]),
61^(1/4)*(Cos[(1/2)*ArcTan[6/5]] +
I*Sin[(1/2)*ArcTan[6/5]])}
FullSimplify[Times@@r]
-5 - 6*I
Bob Hanlon
>
> From: ivan.svaljek at gmail.com
To: mathgroup at smc.vnet.net
> Subject: [mg64199] [mg64181] Re: Trigonometric form of complex numbers
>
> I'm looking for a solution that would produce something like this:
> r (cos f + i sin f).
>
> And would return n roots of a complex number in such form.
>
> Mathematica itself does nothing to return roots of complex numbers. Am
> I wrong ?
>
>
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