complex-numbers¶

; Arithmetic
(define (add-complex z1 z2)
    (make-from-real-imag (+ (real-part z1) (real-part z2))
                         (+ (imag-part z1) (imag-part z2))))

(define (sub-complex z1 z2)
    (make-from-real-imag (- (real-part z1) (real-part z2))
                         (- (imag-part z1) (imag-part z2))))

(define (mul-complex z1 z2)
    (make-from-mag-ang (* (magnitude z1) (magnitude z2))
                       (+ (angle z1) (* angle z2))))

(define (div-complex z1 z2)
    (make-from-mag-ang (/ (magnitude z1) (magnitude z2))
                       (- (angle z1) (* angle z2))))

; Representation
; (1) In Coordinate form
(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))))

; (2) In polar form
(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))

; Tagged data
(define (attach-tag type-tag contents)
    (cons type-tag contents))

(define (type-tag datum)
    (if (pair? datum)
        (car datum)
        (error "Bad tagged datum: TYPE-TAG" datum)))
(define (contents datum)
    (if (pair? datum)
        (cdr datum)
        (error "Bad tagged datum: CONTENTS" datum)))
(define (rectangular? z)
    (eq? (type-tag z) 'rectangular))
(define (polar? z) (eq? (type-tag z) 'polar))

; Ben's revised rectangular representation
(define (real-part-rectangular z) (car z))
(define (imag-part-rectangular z) (cdr z))
(define (magnitude-rectangular z)
  (sqrt (+ (square (real-part-rectangular z))
           (square (imag-part-rectangular z)))))
(define (angle-rectangular z)
    (atan (imag-part-rectangular z)
          (real-part-rectangular z)))
(define (make-from-real-imag-rectangular x y) (attach-tag 'rectangular (cons x y)))
(define (make-from-mag-ang-rectangular r a)
    (attach-tag 'rectangular
                (cons (* r (cos a)) (* r (sin a)))))

; Alyssa's revised polar representation
(define (real-part-polar z)
    (* (magnitude-polar z) (cos (angle-polar z))))
(define (imag-part-polar z)
    (* (magnitude-polar z) (sin (angle-polar z))))
(define (magnitude-polar z) (car z))
(define (angle-polar z) (cdr z))
(define (make-from-real-imag-polar x y)
  (attach-tag 'polar
              (cons (sqrt (+ (square x) (square y)))
                    (atan y x)))) 
(define (make-from-mag-ang-polar r a)
  (attach-tag 'polar (cons r a)))

; Generic selectors
(define (real-part z)
    (cond ((rectangular? z)
           (real-part-rectangular (contents z)))
          ((polar? z)
           (real-part-polar (contents z)))
          (else (error "Unknown type: REAL-PART" z))))
(define (imag-part z)
    (cond ((rectangular? z)
           (imag-part-rectangular (contents z)))
          ((polar? z)
           (imag-part-polar (contents z)))
          (else (error "Unknown type: IMAG-PART" z))))
(define (magnitude z)
    (cond ((rectangular? z)
           (magnitude-rectangular (contents z)))
          ((polar? z)
           (magnitude-polar (contents z)))
          (else (error "Unknown type: MAGNITUDE" z))))
(define (angle z)
    (cond ((rectangular? z)
           (angle-rectangular (contents z)))
          ((polar? z)
           (angle-polar (contents z)))
          (else (error "Unknown type: ANGLE" z))))

(define (make-from-real-imag x y)
    (make-from-real-imag-rectangular x y))
(define (make-from-mag-ang r a)
    (make-from-mag-ang-polar r a))