Yeah, you can view complex numbers as 2d vectors. In this view, you can choose a complex number with a magnitude of 1, at some angle θ to the x-axis (the real line). If you multiply this number by another complex number, it will rotate that number by the angle θ. We can express such a complex number as cosθ + i sinθ.

If you express such a complex number as a 2x2 matrix (there is a unique 2x2 matrix for each complex number, such that the complex number a + ib becomes the matrix

    [ a, b
     -b, a ]

you'll notice that the matrix form of our unitary (magnitude 1) complex number is just a rotation matrix like the one discussed in the article.