#5682 rectform(atan2(y,0)) is 3*%pi/2 for y < 0

[David Scherfgen]

By Claude:

rectform of atan2(y,0) for a real y gives a complicated expression that is wrong for negative y:

(%i1) rectform(atan2(y, 0));
(%o1) (2*%pi*ceiling((2*atan2(0,y)-%pi)/(2*%pi))+%pi)/2-%i*log(abs(y)/sqrt(y^2))
(%i2) subst(y = -2, %);
(%o2) (3*%pi)/2

atan2(-2, 0) is -%pi/2. Also, the imaginary part -log(abs(y)/sqrt(y^2)) is zero for every real y but is not simplified. For a real y, atan2(y, 0) is real, so its rectangular form is atan2(y, 0) itself.