Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 22
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50SCO: By the end of grade
Elaborations - Instructional Strategies/Suggestions
12, students will be
Products and Quotients of Complex Numbers in Polar Form (9.7)
expected to:
Product of complex numbers in polar form:
θ
θ
θ
θ
+
⋅
+
B42 multiply and divide
r
(cos
i
sin
)
r
(cos
i
sin
)
1
1
2
2
2
2
complex numbers in
θ
θ
=
⋅
i
i
polar form
r e
r e
1
2
1
2
θ θ
+
=
i
(
)
r r e
1
2
1 2
θ
θ
θ
θ
=
+
+
+
r r
[cos(
)
i
sin(
)]
1 2
1
2
1
2
θ
θ
=
+
r r cis
(
)
1 2
1
2
The modulus (r
r
) of the product of 2 complex numbers is the
1
2
product of their modulii.
2
2
The argument or amplitude (
+
) of the product of 2 complex
1
2
numbers is the sum of their arguments.
θ
θ
⋅
r cis
r cis
1
1
2
2
θ
θ
=
+
Thus
r r cis
(
)
1 2
1
2
⋅
o
o
4
cis
45
5 15
cis
Ex.
=
o
20
cis
60
Quotient of complex numbers in polar form:
θ
θ
+
r
(cos
i
sin )
1
1
1
θ
θ
+
r
(cos
i
sin
)
2
2
2
r
θ θ
−
=
i
(
)
1
e
1
2
r
2
r
θ
θ
θ
θ
=
−
+
−
1
[cos(
)
i
sin(
)]
1
2
1
2
r
2
r
θ
θ
=
−
1
cis
(
)
1
2
r
2
The modulus of the quotient of 2 complex numbers is the quotient of
their modulii. The argument is the difference of their arguments.
22
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