



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) = a^{2}  b^{2}






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 
