You're clearly confusing what they mean when they say "sum". They're talking about summing the waves in the time domain, not producing a wave at the sum of the frequencies. This should be quite obvious if you actually took the time to draw it out on graph paper as was already suggested.
You are confusing this with a MIXER, as nigel pointed out, which MULTIPLIES the two signals together. This is what produces the sum and difference frequencies. The different signals at different frequencies that a mixer produces are all present in the output as the SUM of the signals. You obviously need to understand the concept of the sum of the signals, as in the simple 2Hz/3Hz case above.
Edit: well just to really lay this to rest (knock on wood) here's a set of plots to help detail what we're all trying to tell you:
Two sinusoidal signals of different frequency
One plot of the SUM of the two signals (what you'd feed a speaker with to hear both sounds at once, the sort of 'complex' signal Nigel is talking about)
One plot of the PRODUCT of the two signals (what you'd get if you fed both into a mixer - notice there's a higher-frequency sine wave 'riding on' a lower-frequency sine wave - these are the sum and difference frequencies)