Complex Numbers Worksheet Page 4
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1
2
3
41.5 Homework Problems
50
1. Simplify each expression: (a)
−
169
(b)
−
200
(c)
−
108
(d)
−
49
27
5
26
7 −
(e)
6 −
(f)
i
(g)
i
(h)
i
4
2. Perform the indicated operation for each problem below. Simplify each problem and write the
answer in standard form.
(a)
3 (
7
i
)
(
8
4
i
)
(b)
6 (
22
i
)
(
9
5
i
)
(c)
3 (
4
i
)(
8
5
i
)
−
+
−
−
−
−
−
+
−
−
+
5
i
2
i
−
−
2
3
(d)
4 (
5
i
)
(e)
(f)
(g)
(h)
2 ( i +
)
−
i
1
+
i
3
+
i
(i)
200
8
(j)
16
25
(k)
3
27
−
+
−
−
⋅
−
−
⋅
−
1
−
18
−
−
27
2
(l)
−
2 (
−
5
i
)
(m)
(n)
2
9
1 (
−
−
) 4
5
2
3. Simplify:
3
2 (
+
3
i
)
−
4. Simplify:
(
x
−
2
+
3
i
)(
x
−
2
−
3
i
)
1
2
i
+
5. Find the reciprocal of 7 + 3 i .
6. Solve each of the following:
2
2
2
2
(a)
x
= x
2
−
17
(b)
2
x
+
5
=
6
x
(c)
9
x
−
24
x
+
8
=
0
(d)
x
+
11
x
=
−
49
5
1.5 Homework Answers: 1. (a) 13 i (b)
10i
2
(c)
6 i
3
(d)
i
2
(e)
9 i
3
(f) i (g) -1
7
1
1
(h) i 2. (a) -5 – 11 i (b) 15 – 27 i (c) -4 + 47 i (d) -9 – 40 i (e) -5 i
(f)
i
−
−
2
2
1
1
3
4
3
(g)
i
(h) 2 + 11 i (i)
12i
2
(j) -20 (k) -9 (l) 21 + 20 i (m)
i
(n)
2 −
i
−
−
+
−
2
2
25
25
3
7
3
3
1
4 ±
2
2
4
2
2
2
3. -16 + 38i 4.
x
− x
4
+
13
5.
−
i
6. (a)
1 ±
i 4
; (b)
±
i
; (c)
or
±
;
58
58
2
2
3
3
3
11
5
3
(d)
i
−
±
2
2
Page 4 (Section 1.5)
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