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July 13th, 2012, 11:14 AM  #11 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: real part of (A+Bi)^(1/3)
You may need to restrict the domain to a onetoone portion of the cubic.

July 13th, 2012, 12:17 PM  #12 
Newbie Joined: May 2012 Posts: 11 Thanks: 0  Re: real part of (A+Bi)^(1/3)
I am restricting it to a onetoone region For example I have... AX^3+BX^2+CX+D=Y where A=3.5855x10^6 B=9.3864x10^5 C=0.17327 D=13.7534 Which is one to one in the region 100<x<300 But when I invert and solve for X I get the above problem in that region 
July 13th, 2012, 12:26 PM  #13 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: real part of (A+Bi)^(1/3)
Differentiating, I find the given cubic is onetoone on the approximate intervals: 
July 13th, 2012, 12:54 PM  #14 
Newbie Joined: May 2012 Posts: 11 Thanks: 0  Re: real part of (A+Bi)^(1/3)
Yes you are correct. Looked again at region from 200<x<300 and this still has a variable K value 
July 13th, 2012, 02:12 PM  #15 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: real part of (A+Bi)^(1/3)
My suggestion was really just thinking out loud. I did have doubts that would fix the problem, but it was the first thing I thought of. I'll give this more consideration.


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