Calculator test

[AnnoyedOne]

(12-13-2024 10:45 PM)naddy Wrote:  I think definitions are generally chosen such that you have the principal value at \(k = 0\).

You (and Albert Chan) are probably correct about that. I forgot about the theta.i term which makes any result complex (vs real) except if theta=0 in which case you get ln(r). k=0 makes things even easier

This stuff is often drawn in 3D so that the 'i' value is simply a rotation about the y-axis (i.e. is on the z-axis). 2.pi is 360 degrees (a full rotation) which gets you back to where you started (just as with trig functions). That is why the value of 'k' really isn't important. Any integer will work. Negative ones just mean rotating in the other direction.

A1