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