Hallo, Chuckk Hubbard hat gesagt: // Chuckk Hubbard wrote:
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))
While doing computations, you can consider i to behave just like a "normal" real number, except if you multiply it with itself, then the result is i*i=-1. That's all there is to know about i.
Because these are the rules for multiplying complex numbers, with z=(a,b)=a+ib you have:
z1*z2 = (a1,b1) * (a2,b2) := (a1 + i*b1) * (a2 + i*b2) = a1a2 + a1*i*b2 + i*b1*a2 + i*i*b1*b2 = a1a2 + i(a1b2 + a2b1) - b1b2 = (a1a2 - b1b2) + i(a1b2 + a2b1) = a3 + i*b3 = z3
so z3 is the complex number pair (a3,b3) or (a1a2 - b1b2, a1b2 + a2b1).
Ciao
Frank Barknecht _ ______footils.org_ __goto10.org__