[Numpy-discussion] arctan2 with complex args

David Goldsmith David.L.Goldsmith@noaa....
Mon Apr 30 10:33:41 CDT 2007


Timothy Hochberg wrote:
>
>
> On 4/30/07, *David Goldsmith* <David.L.Goldsmith@noaa.gov 
> <mailto:David.L.Goldsmith@noaa.gov>> 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
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>
>
>
> -- 
>
> //=][=\\
>
> tim.hochberg@ieee.org <mailto:tim.hochberg@ieee.org>
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