§7.6 Assignment
Notes
1. Exercises from 7.6
2. Nov 20 - Exam #3 Chapter 6,7, Cumulative 5
Exam 3 Study Guide: p 447 Chapter 6 Test: 1 - 12, 16 - 21;
p 507 Chapter 7 Test: 1 - 13, 17 - 21;
p 508 Cumulative Test 5 -7: 1- 18, 23 - 31, 36 -39;
Reminder: The variable expressions in a sum are the terms, and the
variable expressions in a product are the factors.
M 1010 §7.6
(Math 1010)
1/7
§7.6 The Imaginary Unit
Notes
When the real number c > 0, the square root of −c (negative c) is
p
√
√ √
√
−c = c(−1) = c · −1 = ci
√
The complex number i = −1 is the imaginary unit. When both a
and b are real numbers, the complex number a + bi is written in
standard form.
To perform operations with square roots of negative numbers, write
them first in i-form:
ai + bi = (a + b)i, ai − bi = (a − b)i, and
(ai)(bi) = (ab)(i 2 ) = (ab)(−1) = −ab.
M 1010 §7.6
(Math 1010)
2/7
§7.6 Negative Square Roots
Notes
Perform the operations. Write answers in standard form.
√
−16 + −36.
√
#2 Exercise 27. −12 −2.
√
√
√
#3 Exericxe 33. −3( −3 + −4).
#1 Exercise 19.
(Math 1010)
√
√
M 1010 §7.6
3/7
§7.6 Adding and Subtracting Complex Numbers
Notes
Perform the operations.
#4 Exercise 55. (4 − 3i) + (6 + 7i)
#5 Exercise 56. (−10 + 2i) + (4 − 7i)
#6 Exercise 59. 13i − (14 − 7i)
M 1010 §7.6
(Math 1010)
4/7
§7.6 Mulitplying and Dividing
i2
= −1,
i3
= −i,
i4
Notes
= 1.
Perform the operation.
#7 Example 7:
√
a. (7i)(−3i), b. (1 − i)( −9)
c. (2 − i)(4 + 3i), d. (3 + 2i)(3 − 2i).
Note the product result for part (d) is a real number. This occurs with
pairs of complex conjugates of the form a + bi and a − bi That is,
(a + bi)(a − bi) = a2 − (bi)2 = a2 + b 2
(Math 1010)
M 1010 §7.6
5/7
§7.6 Mulitplying and Dividing
Notes
To write a quotient in standard form, multiply the numerator and
denominator both with the complex conjugate of the denominator.
Examples
2 − i (−4i)
2−i
=
·
4i
4i
(−4i)
−8i + 4i 2
=
−16i 2
−8i − 4
=
16
−1
=
− 12i
4
(Math 1010)
M 1010 §7.6
6/7
§7.6 Mulitplying and Dividing
Notes
Multiply the number by its complex conjugate:
# 8 Exercise 111: −2 − 8i.
Write the quotient in standard form:
20
2i
4 + 5i
# 10 Exercise 137:
3 − 7i
# 9 Exercise 123:
(Math 1010)
M 1010 §7.6
7/7
Notes
Notes