Precalculus - Chapter 6 Trigonometry Worksheet With Answers Page 2
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4PRECALCULUS
Name______________________
Chapter 6: Additional Topics in Trigonometry
Date____________ Period______
Example 2: Writing a Complex Number in Trigonometric Form
III. – MULTIPLICATION AND DIVISION OF
Write the complex number z = 3i in trigonometric form.
COMPLEX NUMBERS
Example 3: Writing a Complex Number in Trigonometric Form
Write the complex number z = 6 – 6i in trigonometric form.
Example 5: Multiplying Complex Numbers in Trig Form
Find the product z
z
of the complex numbers:
1
2
π
π
π
π
⎛
⎞
⎛
⎞
3
3
=
+
=
+
z
⎜
i
⎟
z
⎜
i
⎟
7
cos
sin
and
3
cos
sin
1
2
⎝
⎠
⎝
⎠
2
2
2
2
Example 4: Writing a Complex Number in Standard Form
π
π
⎛
⎞
2
2
=
+
z
⎜
i
⎟
Write the complex number
8
cos
sin
in standard
⎝
⎠
3
3
form a + bi.
Example 6: Multiplying Complex Numbers in Trig Form
Find the product z
z
of the complex numbers:
1
2
π
π
π
π
⎛
⎞
⎛
⎞
=
+
=
+
z
⎜
i
⎟
z
⎜
i
⎟
3
cos
sin
and
4
cos
sin
1
2
⎝
⎠
⎝
⎠
3
3
6
6
13
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