Complex Numbers Worksheet
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6Math 96–Complex Numbers–page #1
A.
Combine Like Terms
a.
2x + 8 + 3x + 7
b.
3 + 9i + 6 + 7i
5x + 15
9 + 16i
c.
4
17i + 5 + 3i
d.
Examples b and c are complex numbers
9
14i
in the form a + bi, the standard form
of a complex number
e.
(7 + 18i) + ( 11 + 2i)
f.
( 20
6i)
(13
4i)
7 + 18i
11 + 2i
20
6i
13 + 4i
4 + 20i
33
2i
g.
Example f is in standard form a + bi, where a = 33 and b = 2
h.
2(3 + 5i)
7(4 + 6i)
6 + 10i
28
42i
22
32i
(standard form a + bi, where a = 22 and b = 32)
i.
14 is a real number. In complex number form, it is 14 + 0i, where a = 14 and b = 0
Homework. Simplify appropriately. Write results in a + bi form.
1.
7 + 6i + 9 + 3i
2.
8 + 5i
12 + 2i
3.
14
8i + 6
15i
4.
19
20i
28
5i
5.
(17 + 3i) + (9 + 7i)
6.
(25 + 9i) + (8
10i)
7.
(14
18i)
(20 + 3i)
8.
( 30 + 12i)
( 6 + 5i)
9.
2(5 + 8i) + 6(3
5i)
10.
7( 1 + 4i)
8(2 + 3i)
11.
In 14 + 3i, what is a? What is b?
12.
In 18
31i, what is a? What is b?
13.
Write the real number 28 in complex number form. What is a? What is b?
14.
Write the real number 39 in complex number form. What is a? What is b?
B.
Definition of the Imaginary Unit.
i.
Definition:
This is called the imaginary unit.
You can never leave the square root of a negative number because the square root of negative one
is defined to be i. Observe the examples.
j.
k.
l.
m.
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