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Adding and Subtracting Complex Numbers Worksheet

Adding and Subtracting Complex Numbers Worksheet
  • Page 1
 1.  
Simplify:
7- 81 - (5 - - 64)
a.
5 + 55i
b.
- 5 + 71i
c.
- 5 - 55i
d.
- 5 - 72i


Solution:

7- 81 - (5 - - 64) = 7 · 9i - (5 - 8i)
[Rewrite in terms of i.]

= 63i - 5 + 8i
[Add.]

= - 5 + 71i


Correct answer : (2)
 2.  
Simplify:
(18 - 2- 16) - (7 - 9- 25)
a.
11 + 37i
b.
11 - 37i
c.
25 - 53i
d.
37 + 11i


Solution:

(18 - 2- 16) - (7 - 9- 25) = (18 - 2 · 4i) - (7 - 9 · 5i)
[Rewrite in terms of i.]

= (18 - 8i) - (7 - 45i)

= (18 - 8i) + (- 7 + 45i)
[-7 + 45i is the additive inverse of 7 - 45i.]

= (18 - 7) + (- 8 + 45)i
[Group like terms.]

= 11 + 37i


Correct answer : (1)
 3.  
Simplify:
(2 + - 9) + (9 + - 49 )
a.
10 + 11i
b.
10 - 11i
c.
11 - 10i
d.
11 + 10i


Solution:

(2 + - 9) + (9 + - 49) = (2 + 3i) + (9 + 7i)
[Rewrite in terms of i.]

= (2 + 9) + (3 + 7)i
[Group like terms.]

= 11 + 10i


Correct answer : (4)
 4.  
|- 8 - 16i| = ?
a.
8-5
b.
245
c.
643
d.
85


Solution:

|-8 - 16i| = (-8)2 +(-16)2
[|a + bi| = a2+b2.]

= 64 + 256

= 320

= 64 . 5 = 85


Correct answer : (4)
 5.  
The value of |-4i + 64| is
a.
16
b.
812
c.
45
d.
80


Solution:

|- 4i + 64| = |64 - 4i|
[Express in the form a + bi.]

= |8 - 4i|

= 82+(-4)2
[|a + bi| = a2+b2.]

= 64 + 16

= 80 = 165

= 45


Correct answer : (3)
 6.  
Simplify: |5 - 4-64|
a.
-32
b.
16
c.
25
d.
1049


Solution:

|5 - 4-64| = |5 - 4 . 8i|
[Rewrite in terms of i.]

= |5 - 32i|

= 52+(-32)2
[|a + bi| = a2+b2.]

= 25 + 1024

= 1049


Correct answer : (4)
 7.  
Which of the following sets of numbers does the number 2 + 5i belong to?
a.
irrational numbers
b.
real numbers
c.
complex numbers
d.
rational numbers


Solution:

2 + 5i is a complex number.
[The calculator shows the exponent at the right.]


Correct answer : (3)
 8.  
Which of the following sets of numbers does the number - 4i belong to?
a.
whole numbers
b.
rational numbers
c.
irrational numbers
d.
pure imaginary numbers


Solution:

- 4i is a pure imaginary number.
[A complex number a + bi is purely imaginary if a = 0 and b ≠ 0.]


Correct answer : (4)
 9.  
What is the absolute value of the complex number 6 + 8i?
a.
68
b.
8
c.
10
d.
6


Solution:

|6 + 8i| = 62+82
[|a + bi| = a2 +b2.]

= 36+64

= 100

= 10


Correct answer : (3)
 10.  
Find the value of |2 - 7i|.
a.
53
b.
- 53
c.
- 4
d.
49


Solution:

|2 - 7i| = 22+(-7)2
[|a + bi| = a2 +b2.]

= 4 + 49

= 53


Correct answer : (1)

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