Complex Numbers Worksheet Page 3
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6Math 96–Complex Numbers–page #3
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Definition of i .
C.
2
s.
Definition:
i = 1
You can never leave i squared in an expression because i squared is defined to be negative one.
2
2
t.
5i = 5( 1) = 5
u.
8i = 8( 1) = 8
Notice, 5 is a real number.
2
2
v.
7i + 11i
w.
17
6i
20i
7i + 11( 1)
17
6i 20( 1)
7i
11
17
6i + 20
11 + 7i
37
6i
where a = 11, b = 7
where 11 is the real number part
and 7i is the imaginary number part
x.
(2 + 3i)(7 + 8i)
y.
(8
3i)(8 + 3i)
2
2
14 + 16i + 21i + 24i
64 + 24i
24i
9i
14 + 16i + 21i + 24( 1)
64 + 24i
24i
9( 1)
14 + 16i + 21i
24
64 + 24i
24i + 9
10 + 37i
73
Notice on y, you multiplied conjugates and your
answer was a rational number! Also notice you
could have multiplied the First and Last terms only
because the Outer and Inner terms will cancel out.
Homework. Simplify appropriately.
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2
31.
a.
7i
b.
12i
2
2
c.
13i + 6i
d.
18 + 10i
7i
32.
(2 + 3i)(4 + 8i)
33.
(7
4i)(3 + 2i)
34.
( 8 + 5i)(6
4i)
35.
(9
2i)(5
3i)
36.
(7 + 5i)(7
5i)
37.
(9
6i)(9 + 6i)
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