Algebra 2 Complex Conjugates
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Do You Have a Complex?
Complex Conjugates

 

 Sometimes you see complex numbers in fractions, 

 like this ...

 

 
 You might be asked to change one of these puppies 
 into something that looks like ...

 a + bi

 
 Can we do it???
 
 No problem!
 Remember something called the difference of two squares?
 It went like this ...

 (a + b) (a - b) = a2 - b2

 
 The nice thing about this is that the middle term cancels out
 and all that you have left are the squared terms.
 
 And remember, i 2 = -1.
 
 If we multiply the complex denominator
 by the other "difference of two squares" factor
 the denominator that we are left with has no "i" in it!
 
 We can't change the value of the fraction,
 so we multiply the fraction by a very special name for 1 ...
 

 

 
 Just think of the "i" as an X or a Y and do the multiplication ...
 

 

 
 i 2 = -1, so ...

 

 
 Now we "split this up," 
 just like we do when we're solving for X ...
 

 

 
 We had 7 - 3i in the denominator.
 We used 7 + 3i to simplify it.
 
 In general, if we have a + bi
 we can use a - bi to simplify it.
 
 In math talk, these are called "complex conjugates" pf each other.
 
 Oh those wascally math names. he he he.
 

   copyright 2005 Bruce Kirkpatrick

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