rtoy
commented
3 months ago Imported from SourceForge on 2024-07-09 17:50:54 Created by crategus on 2010-08-22 18:35:31 Original: https://sourceforge.net/p/maxima/bugs/2053/#028e
Fixed in rpart revision 1.36.
Now we get
(%i7) carg(exp(x+%i*y)); (%o7) atan2(sin(y),cos(y))
The most general case is:
(%i8) declare([z1,z2],complex);
(%i9) carg(z1^z2); (%o9) atan2(sin('carg(z1)*'realpart(z2)+log(abs(z1))*'imagpart(z2)), cos('carg(z1)*'realpart(z2)+log(abs(z1))*'imagpart(z2)))
Dieter Kaiser
Imported from SourceForge on 2024-07-09 17:50:53 Created by crategus on 2010-08-07 17:04:58 Original: https://sourceforge.net/p/maxima/bugs/2053
I think the following result is not correct in general:
(%i1) carg(exp(x+%i*y)); (%o1) y
It is only valid for -%pi < y <= %pi.
This is a simple example:
(%i2) carg(exp(n*%pi*%i)); (%o2) %pi*n
The above result is correct for n=1, but not for n=2. For n=2 we have exp(2*%pi*%i) -> 1. carg(1) is zero and not 2*%pi.
A more correct simplification would be
carg(exp(x+%i*y)) --> atan2(sin(y),cos(y))
Dieter Kaiser