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(3+2i)/(5+4i)

If you multiply both sides by the conjugate of the denominator (5-4i), you get:

(3+2i)(5-4i)/(5+4i)(5-4i)

= (23-2i)/(25 + 16 +20i - 20i)

= (23-2i)/41

The denominator is now real, because the i terms cancel

As a general formula (easy to expand) this would be:

(a+bi)/(c+di) = [(ac+bd) + (bc-ad)i] / (c^2 + d^2)

It's a very easy method, but if you're the sort of person who loves using general formulas, there it is.

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