My Math Forum real part of (A+Bi)^(1/3)

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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 one-to-one 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 one-to-one 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
 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 one-to-one on the approximate intervals: $$$-\infty,-135.945$$,\,$$-135.945,118.492$$,\,$$118.492,\infty$$$
 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
 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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