5.7 Complex Numbers Worksheet With Answer Key Page 3
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1
2
3Multiply Complex Numbers
To multiply two complex numbers, use the
Extra Example 4
distributive property or the FOIL method.
Write the expression as a complex
number in standard form.
EXAMPLE
4
Multiply Complex Numbers
a. 25i (8 2 9i )
245 2 40i
b. (28 1 2i )(4 2 7i )
218 1 64i
Write the expression as a complex number in standard form.
2i( 1
3i)
(6
3i)(4
3i)
a.
b.
Key Question to Ask
Solution
for Example 4
• If you use the FOIL method to
2
2i( 1
3i)
2i
6i
Multiply using distributive property.
a.
multiply two complex numbers
of the form a 1 bi and c 1 di,
2
2i
6( 1)
Use
i
1.
which of the products F, O, I, and
6
2i
Write in standard form.
L contribute to the real part of
2
(6
3i)(4
3i)
24
18i
12i
9i
b.
Multiply using FOIL.
the product, and which products
contribute to the imaginary part?
2
24
6i
9i
Simplify.
real part: F and L; imaginary
2
24
6i
9( 1)
i
Use
1.
part: O and I
33
6i
Write in standard form.
Extra Example 5
3 1 4i
}
Write
as a complex number in
5 2 4i
Two complex numbers of the form a
bi and a
bi
Complex Conjugates
1
32
2
1
are called complex conjugates. The product of complex conjugates is always
}
}
standard form.
i
41
41
a real number. You can use complex conjugates to write the quotient of two
complex numbers in standard form.
Closing the Lesson
Have students summarize the
EXAMPLE
5
Divide Complex Numbers
major points of the lesson and
answer the Essential Question:
3
2i
Write
as a complex number in standard form.
How do you perform operations
1
2i
on complex numbers?
To add or
Solution
subtract complex numbers, add
3
2i
3
2i
1
2i
Multiply the numerator and the denominator
or subtract their real parts and
STUDENT HELP
1
2i
1
2i
1
2i
by 1
2i, the complex conjugate of 1
2i.
their imaginary parts separately.
S
N
OLVING
OTE
To multiply complex numbers, use
Notice that the result of
2
3
6i
2i
4i
Multiply using FOIL.
multiplying a complex
the distributive property or the
2
1
2i
2i
4i
number by its complex
FOIL method. To divide complex
conjugate is very similar
numbers, multiply the numerator
3
8i
4( 1)
2
Simplify and use i
1.
to the difference of two
and denominator by the complex
1
4( 1)
squares pattern used to
conjugate of the denominator.
multiply binomials.
1
8i
Simplify.
5
1
8
i
Write in standard form.
5
5
Checkpoint
Multiply and Divide Complex Numbers
Write the expression as a complex number in standard form.
2
i
1
3
3i(2
i)
(1
2i)(2
i)
13.
3
6i
14.
4
3i
15.
i
1
i
2
2
5.7 Complex Numbers
263
263
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