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(b)

Solution (a)

The value of r is

and since and , it follows from 1 that

so and . The only value of that satisfies these relations and meets the requirement is
(see Figure 10.3.2a). Thus a polar form of z is

Solution (b)

The value of r is

and since , , it follows from 1 that

so and . The only value of that satisfies these relations and meets the requirement
is (Figure 10.3.2b). Thus, a polar form of z is

Figure 10.3.2

Multiplication and Division Interpreted Geometrically

We now show how polar forms can be used to give geometric interpretations of multiplication and division of complex
numbers. Let