﻿ Adding and Subtracting Complex Numbers Worksheet | Problems & Solutions

# Adding and Subtracting Complex Numbers Worksheet

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

#### Solution:

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

= 63i - 5 + 8i

= - 5 + 71i

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

#### 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

3.
Simplify:
(2 + ) + (9 + )
 a. 10 + 11$i$ b. 10 - 11$i$ c. 11 - 10$i$ d. 11 + 10$i$

#### Solution:

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

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

= 11 + 10i

4.
|- 8 - 16$i$| = ?
 a. 8$\sqrt{-5}$ b. 24$\sqrt{5}$ c. 64$\sqrt{3}$ d. 8$\sqrt{5}$

#### Solution:

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

= 64 + 256

= 320

= 64 . 5 = 85

5.
The value of |-4$i$ + $\sqrt{64}$| is
 a. 16 b. 8$\sqrt{12}$ c. 4$\sqrt{5}$ 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

6.
Simplify: |5 - 4$\sqrt{-64}$|
 a. $\sqrt{-32}$ b. 16 c. $\sqrt{25}$ d. $\sqrt{1049}$

#### Solution:

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

= |5 - 32i|

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

= 25 + 1024

= 1049

7.
Which of the following sets of numbers does the number 2 + 5$i$ 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.]

8.
Which of the following sets of numbers does the number - 4$i$ 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.]

9.
What is the absolute value of the complex number 6 + 8$i$?
 a. 6$\sqrt{8}$ b. 8 c. 10 d. 6

#### Solution:

|6 + 8i| = 62+82
[|a + bi| = a2 +b2.]

= 36+64

= 100

= 10

10.
Find the value of |2 - 7$i$|.
 a. $\sqrt{53}$ b. - 53 c. - 4 d. $\sqrt{49}$

#### Solution:

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

= 4 + 49

= 53