lorenzo bolla wrote:
me!
I have two cases.
1. I need that arctan2(1+0.0001j,1-0.01j) gives something
close to arctan2(1,1): any decent analytic prolungation will do!
This is the foreseeable use case described by Anne.
In any event, I stand not only corrected, but
On 4/30/07, David Goldsmith [EMAIL PROTECTED] wrote:
(hint what is arctan(0+1j)?)
Well, at the risk of embarrassing myself, using arctan(x+iy) = I get:
arctan(0+1i) = -i*log((0+i*1)/sqrt(0^2 + 1^2)) = -i*log(i/1) = -i*log(i)
= -i*log(exp(i*pi/2)) = -i*i*pi/2 = pi/2...
Is there some reason
hold on, david. the formula I posted previously from wolfram is ArcTan[x,y]
with x or y complex: its the same of arctan2(x,y). arctan is another
function (even though arctan2(y,x) should be a better arctan(y/x)).
the correct formula for y = arctan(x), with any x (real or complex), should
be (if
lorenzo bolla wrote:
hold on, david. the formula I posted previously from wolfram is
ArcTan[x,y] with x or y complex: its the same of arctan2(x,y). arctan
is another function (even though arctan2(y,x) should be a better
arctan(y/x)).
the correct formula for y = arctan(x), with any x (real
Timothy Hochberg wrote:
On 4/30/07, *David Goldsmith* [EMAIL PROTECTED]
mailto:[EMAIL PROTECTED] wrote:
(hint what is arctan(0+1j)?)
Well, at the risk of embarrassing myself, using arctan(x+iy) = I get:
arctan(0+1i) = -i*log((0+i*1)/sqrt(0^2 + 1^2)) = -i*log(i/1) =
Weird behaviour with arctan2(complex,complex).
Take a look at this:
In [11]: numpy.arctan2(1.,1.)
Out[11]: 0.785398163397
In [12]: numpy.arctan2(1j,1j)
---
exceptions.AttributeErrorTraceback
I'll take a stab at this one; if I miss the mark, people, please chime in.
What's strange here is not numpy's behavior but octave's (IMO).
Remember that, over R, arctan is used in two different ways: one is
simply as a map from (-inf, inf) - (-pi/2,pi/2) - here, let's call that
invtan; the
Far be it from me to challenge the mighty Wolfram, but I'm not sure that
using the *formula* for calculating the arctan of a *single* complex
argument from its real and imaginary parts makes any sense if x and/or y
are themselves complex (in particular, does Lim(formula), as the
imaginary part
On 29/04/07, David Goldsmith [EMAIL PROTECTED] wrote:
Far be it from me to challenge the mighty Wolfram, but I'm not sure that
using the *formula* for calculating the arctan of a *single* complex
argument from its real and imaginary parts makes any sense if x and/or y
are themselves complex
