Multiplying any two complex numbers 'a' and 'b' gives you a complex number z whose magnitude is the magnitude of 'a' times the magnitude of 'b' (that's covered in the article). I always thing of a 'complex conjugate' as a reflection across the real number line (i.e. has the opposite angle or 'phase'), so when a complex number and its conjugate are multiplied the angle disappears and you're left with no imaginary component, thus just the real part which IS the magnitude. (As a^2 + 0 = c^2)

I hadn't worked with complex numbers much for most of my life, but getting into quantum computing recently it is ALL complex numbers (and linear algebra). It's fascinating (for a certain mindset at least, which I guess I fall into), but it is a lot of mental work and repetition before it starts to feel in any way 'comfortable'.