Vibrations and Waves · Problem 1-2

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

(

z_2 \neq 0

), where

z_1 = a + jb

z_2 = c + jd

. (a) Show that the length of

z

is the quotient of the lengths of

z_1

and

z_2

. (b) Show that the angle between

z

and the

x

axis is the difference of the angles made by

z_1

and

z_2

separately.