simplify roots of exact powers of gaussian integers
Subject: simplify roots of exact powers of gaussian integers
From: Barton Willis
Date: Mon, 10 Sep 2012 12:14:08 +0000
Does Maxima have a way to simplify roots of gaussian integers that are exact powers? Specifically,
is there a way to simplify (expand((5+%i)^3))^(1/3) ---> 5 + %i?
(%i18) e : (expand((5+%i)^3))^(1/3);
(%o18) (74*%i+110)^(1/3)
This doesn't work (but I think it's not incorrect):
(%i41) ratsimp(radcan(exponentialize(logarc(rectform(e))))), algebraic : true;
(%o41) ((55-37*%i)^(5/6)*(37*%i+55)^(1/6)*(37*sqrt(2)*sqrt(13)*%i+55*sqrt(2)*sqrt(13)))/4394
--Barton