[1] In actual computational systems, rectangular form is preferable to polar form most of the time because of roundoff errors in conversion between rectangular and polar form. This is why the complex-number example is unrealistic. Nevertheless, it provides a clear illustration of the design of a system using generic operations and a good introduction to the more substantial systems to be developed later in this chapter.
[2] The arctangent function referred to here, computed by JavaScript's math_atan2 function, is defined so as to take two arguments $y$ and $x$ and to return the angle whose tangent is $y/x$. The signs of the arguments determine the quadrant of the angle.
2.4.1 Representations for Complex Numbers