1. The problem statement, all variables and given/known data Consider a vector z defined by the equation z=z1z2, where z1=a+ib, z2=c+id. (a) show that the length 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 the angles made by z1 and z2 separately. 3. The attempt at a solution (a) i want to just do regular multiplication. (a+ib)(c+id)= ac-bd+i(ad+bc) however i dont see how that would show the length of z is the product of z1 and z2, all i did was multiply. my next idea would be to take the magnitudes of z1 and z2 and multiply them. so, (√[a^2+(ib)^2]) * (√[c^2+(id)^2]) = (√[a^2-b^2])(√[c^2-d^2]). (b)this would depend in part on which attempt of part (a) is correct. this is because depending on the correct way vector z is represented with its components the angle is going to be different. Thank you in advance.