# Homework Help: Show the length of vector z is the product of z1 and z2.

1. Jun 11, 2013

### bfusco

1. The problem statement, all variables and given/known data
consider a vector z defined by the equation z=z1z2, where z1=a+jb, and z2=c+jd (j=complex: same as 'i').
(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.

P.S. this question is part of a personal study, so feel free to bring all information applicable without skipping steps, as to really solidify my understanding because i have to admit ive gotten to these 'upper level' math and physics classes and i feel as though i know nothing. lol

3. The attempt at a solution
first off considering that this is 2 vectors being multiplied to get another vector im assuming that this is the cross product. if that is the case than i would start by simply taking the determinant resulting in: ad-cb, but at i wouldnt know what to do past this point.

2. Jun 11, 2013

### Staff: Mentor

I don't believe that the cross product is called for here, and I also believe that the description of z as a vector is somewhat misleading. You are given that z1 and z2 are complex numbers, for which ordinary multiplication is defined.

3. Jun 11, 2013

### Dick

It's really pretty easy if you express the complex numbers in polar form, if you gotten that far and want a shortcut.

Last edited: Jun 11, 2013