> > > Ramiro is right - that is, his text is much better than the > present text. However normalizations differ. > > It is true that tan(carg(z)) = cimag(z) / creal(z), > almost by definition. Taking atan() on both sides yields > atan(tan(carg(z))) = atan(cimag(z) / creal(z)) > but it is not precisely true that atan(tan(x)) = x. > The tan() function is periodic with period pi, and > atan() returns an answer in (-pi/2,pi/2], so atan(tan(x)) > returns the value that is congruent x mod pi and lies in > this interval. > In particular, atan(tan(carg(z))) returns a value that > is congruent carg(z) mod pi and lies in (-pi/2,pi/2]. > On the other hand, carg returns a value in [-pi,pi] > and if that return value does not lie in (-pi/2,pi/2] > then carg(z) and atan(cimag(z) / creal(z)) will differ by pi. > > In other words: you may write > "One has tan(carg(z)) = cimag(z) / creal(z)." > > Andries > >
Hello Andries, your explanation is superb and very accurate. You are completely right. I never thought I could find a bug.....;-) Free software and Debian are marvellous. Thank you very much. Ramiro. -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
