Exercise 2.77: Louis Reasoner tries to evaluate
the expression (magnitude z) where z is the object shown in
Figure 2.24.  To his surprise, instead of the answer 5 he gets an error
message from apply-generic, saying there is no method for the operation
magnitude on the types (complex).  He shows this interaction to
Alyssa P. Hacker, who says “The problem is that the complex-number selectors
were never defined for complex numbers, just for polar and
rectangular numbers.  All you have to do to make this work is add the
following to the complex package:”


(put 'real-part '(complex) real-part)
(put 'imag-part '(complex) imag-part)
(put 'magnitude '(complex) magnitude)
(put 'angle '(complex) angle)

Describe in detail why this works.  As an example, trace through all the
procedures called in evaluating the expression (magnitude z) where
z is the object shown in Figure 2.24.  In particular, how many
times is apply-generic invoked?  What procedure is dispatched to in each
case?