복소수 하나는 서로 유용한 두 좌표계를 가질 수 있다.

(begin
  (define (square x) (* x x))
  (define (close? left right)
    (< (abs (- left right)) 0.000001))
  (define (attach-tag type contents) (cons type contents))
  (define (type-tag object) (car object))
  (define (contents object) (cdr object))
  (define (make-from-real-imag x y)
    (attach-tag 'rectangular (list x y)))
  (define (make-from-mag-ang magnitude angle)
    (attach-tag 'polar (list magnitude angle)))
  (define (rectangular-real z) (car z))
  (define (rectangular-imag z) (cadr z))
  (define (rectangular-magnitude z)
    (sqrt (+ (square (rectangular-real z))
             (square (rectangular-imag z)))))
  (define (rectangular-angle z)
    (atan (rectangular-imag z) (rectangular-real z)))
  (define (polar-magnitude z) (car z))
  (define (polar-angle z) (cadr z))
  (define (polar-real z)
    (* (polar-magnitude z) (cos (polar-angle z))))
  (define (polar-imag z)
    (* (polar-magnitude z) (sin (polar-angle z))))
  (define (select object rectangular-selector polar-selector)
    (cond ((eq? (type-tag object) 'rectangular)
           (rectangular-selector (contents object)))
          ((eq? (type-tag object) 'polar)
           (polar-selector (contents object)))
          (else (error "unknown complex representation"))))
  (define (real-part z) (select z rectangular-real polar-real))
  (define (imag-part z) (select z rectangular-imag polar-imag))
  (define (magnitude z)
    (select z rectangular-magnitude polar-magnitude))
  (define (angle z) (select z rectangular-angle polar-angle))
  (define rectangular (make-from-real-imag 3.0 4.0))
  (define polar (make-from-mag-ang 5.0 (atan 4.0 3.0)))
  (list (type-tag rectangular)
        (type-tag polar)
        (close? (real-part rectangular) (real-part polar))
        (close? (imag-part rectangular) (imag-part polar))
        (close? (magnitude rectangular) (magnitude polar))
        (close? (angle rectangular) (angle polar))))