Alg_Complete

# So we need to get the is out of the denominator this

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Unformatted text preview: lied a number by its conjugate. There is a nice general formula for this that will be convenient when it comes to discussion division of complex numbers. ( a + bi ) ( a - bi ) = a 2 - abi + abi - b2i 2 = a 2 + b 2 So, when we multiply a complex number by its conjugate we get a real number given by, ( a + bi )( a - bi ) = a 2 + b 2 Now, we gave this formula with the comment that it will be convenient when it came to dividing complex numbers so let’s look at a couple of examples. Example 3 Write each of the following in standard form. 3-i (a) [Solution] 2 + 7i 3 (b) [Solution] 9-i 8i (c) [Solution] 1 + 2i 6 - 9i (d) [Solution] 2i Solution So, in each case we are really looking at the division of two complex numbers. The main idea here however is that we want to write them in standard form. Standard form does not allow for any i's to be in the denominator. So, we need to get the i's out of the denominator. This is actually fairly simple if we recall that a complex number times its conjugate is a real number. So, if we multiply the n...
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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.

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