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2.4.1 Representations for Complex Numbers

Rectangle

(define (real-part z) (car z))
(define (imag-part z) (cdr z))

(define (magnitude z)
  (sqrt (+ (square (real-part z)) 
           (square (imag-part z)))))

(define (angle z)
  (atan (imag-part z) (real-part z)))

(define (make-from-real-imag x y) 
  (cons x y))

(define (make-from-mag-ang r a)
  (cons (* r (cos a)) (* r (sin a))))

Polar

(define (real-part z)
  (* (magnitude z) (cos (angle z))))

(define (imag-part z)
  (* (magnitude z) (sin (angle z))))

(define (magnitude z) (car z))
(define (angle z) (cdr z))

(define (make-from-real-imag x y)
  (cons (sqrt (+ (square x) (square y)))
        (atan y x)))

(define (make-from-mag-ang r a) 
  (cons r a))