Page 791 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Multiplying, we obtain
Recalling the trigonometric identities

we obtain

which is a polar form of the complex number with modulus and argument . Thus we have shown that (3)
(4)

and

(Why?) In words, the product of two complex numbers is obtained by multiplying their moduli and adding their arguments
(Figure 10.3.3).

We leave it as an exercise to show that if , then

(5)

from which it follows that

and

In words, the quotient of two complex numbers is obtained by dividing their moduli and subtracting their arguments (in the
appropriate order).

Figure 10.3.3
The product of two complex numbers.

EXAMPLE 2 A Quotient Using Polar Forms
Let
Polar forms of these complex numbers are