Posted by Michael on Monday, April 30, 2012 at 10:31pm.
First, multiply both the numerator (top) and denominator (bottom) by the equivalent of 1 to eliminate i in the denominator:
(5 - 9i)(5 - 2i)
----------------
(5 + 2i)(5 - 2i)
25 - 55i + 18i^2
----------------
25 - 4i^2
Remember that i^2 = -1
25 - 55i + 18(-1)
-----------------
25 - 4(-1)
25 - 55i - 18
-------------
25 + 4
7 - 55i
-------
29
You can change this to standard form if asked to do so.
I hope this helps.
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