The complex conjugate $z^*$ of a complex number $z=x+iy$ is found by replacing every $i$ by $-i$. Therefore $z^*=x-iy$. (A common alternate notation for $z^*$ is $\bar{z}$.) Geometrically, you should be able to see that the complex conjugate of ANY complex number is found by reflecting in the real axis. Add a figure showing complex conjugates and the distance of z and zbar from the origin.

Now let's calculate the product \begin{eqnarray} z z^*&=&(x+iy)(x-iy)\\ &=&x^2+y^2\\ &=&\vert z \vert^2 \end{eqnarray} Notice that this product is ALWAYS a positive, real number. The (positive) square root of this number is the distance of the point $z$ from the origin in the complex plane. We call the square root the norm or magnitude of $z$ and we use the same notation as “absolute value,” i.e. $\vert z\vert$. In this way, we see that the definition of absolute value, as in $\vert -2\vert=2$, was never “strip off the minus sign,” but really “how far is $-2$ from the origin.