Complex number

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