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real numbers are simply a subset of the complex numbers.
The conjugate of the complex number a + bi is the complex number a  bi . In other words, it
is the original complex number with the sign on the imaginary part changed. Here are some
examples of complex numbers and their conjugates. complex number
1
3+ i
2
12  5i
1 i
45i
101 conjugate
1
3 i
2
12 + 5i
1+ i
45i
101 Notice that the conjugate of a real number is just itself with no changes.
Now we need to discuss the basic operations for complex numbers. We’ll start with addition and
subtraction. The easiest way to think of adding and/or subtracting complex numbers is to think of
each complex number as a polynomial and do the addition and subtraction in the same way that
we add or subtract polynomials. Example 1 Perform the indicated operation and write the answers in standard form.
(a) ( 4 + 7i ) + ( 5  10i )
(b) ( 4 + 12i )  ( 3  15i )
(c) 5i  ( 9 + i )
Solution
There really isn’t much to do here other than add or subtract. Note that the parentheses on the
first terms are only there to indicate t...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
 Spring '12
 MrVinh

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