5.7 Complex Numbers Worksheet With Answer Key Page 2
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1
2
3Complex Numbers
A complex number written in standard form is a number
3
TEACH
a
bi where a and b are real numbers. The number a is the real part of the complex
number. The number bi is the imaginary part. The diagram below shows the
different types of complex numbers.
Extra Example 1
Complex Numbers (a 1 bi )
Solve the equation.
Imaginary numbers
Real numbers are
}
}
5 290
23i Ï
5 , 3i Ï
Real
Imaginary
2
a. 2x
5
complex numbers
always have an
Numbers
Numbers
}
}
2 8 5 232
22i Ï
2 , 2i Ï
that have no
imaginary part
2
b. 3x
2
(a 1 0i )
(a 1 bi, b Þ 0)
imaginary part
(b
0).
2 1 3i
5 2 5i
(b
0).
Key Question to Ask
5
5
21
Pure imaginary
Pure
2
2
for Example 1
numbers have no
Imaginary
Numbers
real part
• In Lesson 5.6, you learned to
(0 1 bi, b Þ 0)
p
0, b
2
(a
0).
solve equations such as
24i
2 11 5 37 by finding square
2
6i
2x
roots. What one additional step
is needed to solve the equation
}
}
Rewrite Ï
28 as i Ï
in part (b)?
8 .
To add complex numbers, add their real parts and
Add Complex Numbers
their imaginary parts separately.
Extra Example 2
Write (12 2 11i ) 1 (28 1 3i ) as a
EXAMPLE
2
Add Complex Numbers
complex number in standard form.
4 2 8i
Write (3
2i)
(1
i) as a complex number in standard form.
Solution
Extra Example 3
(3
2i)
(1
i)
(3
1)
(2
1)i
Group real and imaginary terms.
Write (15 2 9i) 2 (24 2 9i) as a
4
i
Write in standard form.
29
complex number in standard form.
Key Question to Ask
To subtract complex numbers, subtract their real
Subtract Complex Numbers
for Examples 2 and 3
parts and their imaginary parts separately.
• What is the standard form of a
It is a 1 bi,
complex number?
EXAMPLE
Subtract Complex Numbers
3
where a and b are real numbers
and i is the imaginary unit.
Write (6
2i)
(1
2i) as a complex number in standard form.
Solution
Differentiated Instruction
(6
2i)
(1
2i)
(6
1)
( 2
2)i
Group real and imaginary terms.
Below Level Ask students to
redraw the diagram on this page
5
0i
Simplify.
to include all the subsets of real
5
Write in standard form.
numbers that are familiar. Have
them refer to the diagram on page 3
of Lesson 1.1.
Checkpoint
Add and Subtract Complex Numbers
Write the expression as a complex number in standard form.
5
5
3i
(4
2i)
(1
3i)
i
(3
i)
(2
4i)
7.
8.
2
3i
4
3i
(4
6i)
(2
3i)
( 2
4i)
(2
7i)
9.
10.
5
3i
3
3i
(1
2i)
(4
5i)
(2
i)
( 1
4i)
11.
12.
262
Chapter 5 Quadratic Functions and Factoring
262
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