Rationalizing Imaginary Denominators

When dealing with fractions with imaginary denominators, one must express this as a complex number in a+bi form.


For example:

17 - 3i
10 + 7i

1) Multiply by the conjugate of the denominator over itself (fraction equals 

17 - 3i   *   (10 - 7i)         
10 + 7i       (10 - 7i)

2)Foil. FOIL the top and FOIL the bottom.

170 - 119i - 30i + 21i²
100 -70i + 70i + 49i²



3)Multiply top by top, bottom by bottom.



170 - 149i + 21i²                 
    100 + 49i²                                

                                                                               
4)Combine the imaginary terms. They (i) 

cancels out in the denominator.


170 - 149i - 21
    100 + 49

5) Combine constant terms on top and bottom.


149 -149i
      149

6)Split apart into a+bi form.

149  -  149   i
149      149



1 - i