Complex number

Basic calculation
For complex numbers C1=a+bi and C2=c+di, where i is (-1)^0.5, a,b, c & d are real numbers.
you can treat it as a 2D calculation
C1+C2=(a+c)+(b+d)i
C1-C2=(a-c)+(b-d)i
C1 x C2 = (a+bi)(c+di)=ac+adi+bci+bdii=(ac-bd)+(ad+bc)i
(same as cases like (x+1)(x+2)=x^2+3x+2, but i^2=-1)
C1/C2=(a+bi)/(c+di)=[(a+bi)(c-di)] / [(c+di)(c-di)]
=(ac-adi+bci-bdii)/(c^2+d^2)=[(ac+bd)+(bc-ad)i]/(c^2+d^2)
(use of complex conjugate, complex conjugate of a+bi is a-bi)
Transform into surd form
a+bi=(a^2+b^2) (a+bi)/(a^2+b^2)
=(a^2+b^2) {[a/(a^2+b^2)]+[b/(a^2+b^2)]i}
=(a^2+b^2) (cos x+isinx)
where cosx = a/(a^2+b^2), sinx=b/(a^2+b^2)
Absolute value
(C1C1*)^0.5, where C1* is complex conjugate of C1
C1C1*=(a+bi)(a-bi)=a^2+b^2
|C1|=(a^2+b^2)^0.5
the basic idea is seperating the real and imaginary part in calculation.

http://mathews.ecs.fullerton.edu/c2000/