Vibrations and Waves · Problem 1-1

The superposition of periodic motions — A.P. French

Physics — Waves · complex-numbers-rotating-vectors

Problem

Consider a vector

z

defined by the equation

z = z_1 z_2

, where

z_1 = a + jb

z_2 = c + jd

. (a) Show that the length of

z

is the product of the lengths of

z_1

and

z_2

. (b) Show that the angle between

z

and the

x

axis is the sum of the angles made by

z_1

and

z_2

separately.