Go to Pauls Online Math Notes - Complex Numbers (Lamar University)

Dawkins clearly explains what complex numbers are and gives examples in the Cartesian coordinate representation. Examples for addition and subtraction are given, also for multiplication (where he shows how to use the fact that i * i = -1). He also explains division, showing how to use the conjugate to make the denominator real. All this is done only in the cartesian coordinates representation, the polar coordinates representation is not covered. But you can find it in another chapter of the same notes (though this chapter is a bit more advanced): Complex Numbers Primer. The most important part of this (if you just need complex numbers to analyse AC circuits), is the section on Polar and Exponential Forms where he shows how to convert between the Cartesian and the polar representation. Strangely, he does not explain multiplication and division using the polar representation, which is really simple: For the multiplication, multiply the magnitudes and add the angles. For the division, divide the magnitudes and subtract the angles.

You may also be interested in some other recommendations for Introductions to Complex Numbers. Dawkins has also written a lot of other excellent math notes, see, for example, his notes on Calculus I.

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