Complex Numbers Worksheet - Appendix F, Cengage Page 7
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APPENDIX F
Complex Numbers
Note that this rule says that to multiply two complex numbers you multiply
moduli and add arguments, whereas to divide two complex numbers you divide
moduli and subtract arguments.
EXAMPLE 7
Multiplying Complex Numbers in Polar Form
Find the product
z
z
of the complex numbers.
1
2
2
2
11
11
z
2 cos
i sin
,
z
8 cos
i sin
2
1
3
3
6
6
Solution
2
2
11
11
z
z
2 cos
i sin
8 cos
i sin
1
2
3
3
6
6
2
11
2
11
16 cos
i sin
3
6
3
6
5
5
16 cos
i sin
2
2
16 cos
i sin
2
2
16 0
i 1
16i
Check this result by first converting to the standard forms
z
1
3i
and
1
z
4 3
4i
and then multiplying algebraically.
2
EXAMPLE 8
Dividing Complex Numbers in Polar Form
Find the quotient
z
z
of the complex numbers.
1
2
z
8 cos 75
i sin 75
z
24 cos 300
i sin 300 ,
2
1
Solution
z
24 cos 300
i sin 300
1
z
8 cos 75
i sin 75
2
24
cos 300
75
i sin 300
75
8
3 cos 225
i sin 225
2
2
3
i
2
2
3 2
3 2
i
2
2
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