Dividing Complex Numbers

How do you divide this: 4/(7 + 2i)?

4
--------
7 + 2i

4 (7 - 2i)
-------------------- {multiplied top and bottom by "conjugate" of denominator}
(7 + 2i)(7 - 2i)

28 - 8i
----------- {used distributive property on top, foil method on bottom}
49 - 4i^2

28 - 8i
------------ {i^2 is -1, when dealing with imaginary numbers}
49 - 4(-1)

28 - 8i
----------- {multiplied -4 by -1}
49 + 4

28 - 8i
---------- {added 49 and 4 on bottom}
53


- Algebra House