1. The problem statement, all variables and given/known data Question from Vibrations and Waves by A.P. French Chapter 1 Consider a vector z defined by Z=Z1Z2, where Z1=a+jb, Z2=c+jd. a)Show that the length of the of z is the product of the lengths of Z1 and Z2. b)Show that the angle between z and the x-axis is the sum of of the angles made by Z1 and Z2 2. Relevant equations tan(θ1)=b/a tan(θ2)=d/c |Z1|=Z1 |Z2|=Z2 3. The attempt at a solution So the first part I didn't have any trouble with, it was fairly straight forward showing that the length of Z1*Z2 was equal to the length of Z. But when I moved to part B I ran into a problem. Here's what I tried. I Knew θ1=b/a and θ2=d/c by a first order taylor expansion of the tangents of these angles and since I am told the angle of Z, θZ is the sum of these two. I must prove: θZ=(cb+da)/ca However when I write out the form of Z=Z1Z2 I get: Z=ac-bd +j(ad+bc). Now since I know the tan(θZ)=imaginary/real I get tan(θZ)=(ad+bc)/(ac-bd). I'm not quite sure what I'm doing wrong, but I'd really appreciate a hand! Thanks!