Carson Elementary And Intermediate Algebra 3e Page 2
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4M098
Carson Elementary and Intermediate Algebra 3e
Section 10.7
2. Perform arithmetic operations with complex numbers.
When the real numbers and the imaginary numbers are combined, they form the complex number
system. Complex numbers are written in the form a + bi, where a is the real part and bi is the imaginary
part.
All of the real numbers that we are familiar with are complex numbers, but because b = 0, we don't write
the imaginary part of the number. 4 is really 4 + 0i .
The imaginary numbers are complex numbers where the real part is equal to 0. The earlier problem that
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we did with
i 7
is technically 0 + 7i. Again, we generally do not write the real part if it is equal
to 0.
The chart on p. 850 is a good visual representation of the system of complex numbers and how the
number types are related.
Just as we learned to add, subtract, multiply and divide each of the other number types, we now learn to
add, subtract, multiply and divide complex numbers. As you work with these, remember that
i
1
not -1. They are not the same thing.
All of the operations should look familiar. The i is treated the same way a variable is treated. You will
add/subtract like terms (i), multiply by foiling and divide by rationalizing the denominator. Same skills, just
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new numbers. Remember whenever you have i
, replace it with -1.
(5 – 3i) + (4 – 5i)
Example 4:
(5 + 4) + (-3i – 5i)
Combine the real parts and the imaginary parts.
9 – 8i
Always write the real part and then the imaginary part.
(8 – 3i) – (-1 – 2i)
Example 5:
8 – 3i + 1 + 2i
Rewrite as an addition problem.
9 – i
Combine the real parts and the imaginary parts.
Example 6:
(4i)(-7i)
2
-28 i
Multiply
2
(-28)(-1)
Replace i
with -1
28
-7i(5 – 8i)
Example 7:
2
-35i + 56 i
Multiply
2
-35i + (56)(-1)
Replace i
with -1
-35i – 56
-56 – 35i
Write in standard a + bi form.
V. Zabrocki 2011
page 2
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