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) = > -i*log(i) > = -i*log(exp(i*pi/2)) = -i*i*pi/2 = pi/2... > > Is there some reason I'm forgetting (e.g., a branch cut convention or > something) why this is wrong? > > > Oops. It may well be OK, I answered too fast (I'd explain my thinking, > but ti would be embarassing). Was it: "pi/2 is outside the range of arctan"? (No worries: I thought of this too when I saw what value fell out of the formula, but then, it's outside the range of the *real-valued* function, but clearly it's not outside the range of the *complex-valued* function.)
DG > However, I believe atan works in general for complex numbers but it > may well have a problem for this specific case. > > I should look at this more closely though since the behaviour near > zero does seem a little odd. No time right now, but maybe later today. > > > DG > _______________________________________________ > Numpy-discussion mailing list > Numpy-discussion@scipy.org <mailto:Numpy-discussion@scipy.org> > http://projects.scipy.org/mailman/listinfo/numpy-discussion > > > > > -- > > //=][=\\ > > [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]> > ------------------------------------------------------------------------ > > _______________________________________________ > Numpy-discussion mailing list > Numpy-discussion@scipy.org > http://projects.scipy.org/mailman/listinfo/numpy-discussion > _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
