Re: Help for a basic problem

From: Bob Walton <see.sig@xxxxxxxxxxxxxxxx>
Date: Wed, 19 Oct 2005 01:18:22 GMT

dm wrote:

Can I get a symbolic formula of x, while x satisfies a complex equation, x^3 = a+b*i, where a and b are real-valued variables?

I was trying to figure it out using x = R_x+I_x*i, but it turns out to be a very complex equation.

If no analytical solution is available, how can I get it, by numerical method?

....
X = (-SQRT(3)*(B^2+A^2)^(1/6)*
           SIN(ATAN2(B,A)/3)-(B^2+A^2)^(1/6)*
           COS(ATAN2(B,A)/3))/2+
    %I*(SQRT(3)*(B^2+A^2)^(1/6)*
           COS(ATAN2(B,A)/3)-(B^2+A^2)^(1/6)*
           SIN(ATAN2(B,A)/3))/2

X = -((B^2+A^2)^(1/6)*
           COS(ATAN2(B,A)/3)-SQRT(3)*(B^2+A^2)^(1/6)*
           SIN(ATAN2(B,A)/3))/2-
    %I*((B^2+A^2)^(1/6)*
           SIN(ATAN2(B,A)/3)+SQRT(3)*(B^2+A^2)^(1/6)*
           COS(ATAN2(B,A)/3))/2

X = (B^2+A^2)^(1/6)*
           COS(ATAN2(B,A)/3)+
    %I*(B^2+A^2)^(1/6)*
           SIN(ATAN2(B,A)/3)

by using solve() and rectform() in Macsyma.
--
Bob Walton
Email: http://bwalton.com/cgi-bin/emailbob.pl
.

References:
- Help for a basic problem
  - From: dm

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