I don't much care, I don't want to define my own math, I just want to know why we mix the real and imaginary parts of a product in one specific case. Z1*Z2=r1r2(cos a + isin a)(cosb + isin b) = r1r2 (cosa*cosb)-(sina*sinb) + i(sina*cosb + cosa*sinb) = r1r2 (cos(a + b) + isin(a + b))

You could indeed say that "entity of your choice = 1/0". But you need a

compelling reason why such a quantity is useful, and various proofs on how it is derived and used. All math depends on certain assumptions and those assumptions are different in different circumstances - aka Euclidian geometry and topology.

Actually, you can say 1+2 = 12 ... and if you are putting together a string in a programming language, that makes sense and is useful, it is a valid operation. Many object oriented programming languages let you redefine basic symbols such as "+ - * /". But string addition wouldn't be very helpful for doing audio math calculations.

So if you want to define your own i, go ahead, but don't you think your calculations are going to turn out better if you follow the normal math definitions?

~David

...

What I'm getting at is that expressing rotation as complex numbers is no different than using cartesian coordinates. Why, when you multiply two points, would one of the multiples turn negative? I see no reason you couldn't say i = 1/0. Then 4*0*i=4. That makes as

much

...

sense.

-- "It is not when truth is dirty, but when it is shallow, that the lover of knowledge is reluctant to step into its waters." -Friedrich Nietzsche, "Thus Spoke Zarathustra"