Question

我有复数的数据表示形式，但是我不知道如何将两个复数相乘。也许有人可以帮我吗？

(define (complex-num a b) 
      (cons a b))
(define (real x) 
      (car x)) 
(define (imag x) 
      (cdr x))

Answer 1

(define (complex-mult a b)
  (make-rectangular (- (* (real-part a) (real-part b)) (* (imag-part a) (imag-part b)))
                    (+ (*(real-part a) (imag-part b)) (*(real-part b) (imag-part a)))))

e，g：

]=> (complex-mult 2+3i 5+2i)

 ;Value: 4+19i

]=> (complex-mult -i +i)

;Value: 1

Answer 2

让我们尝试将两个复数相乘

(a + bi) * (c + di) = (a + bi) * c + (a + bi) * di
                    = ac + bci  + adi + bdii
                    = ac + bci + adi - bd     (here we use that i*i = -1)
                    = ac-bd + (bc+ad)i

如果我们将z1=a+bi和z2=c+di放进去，我们可以将其翻译为Scheme：

(define (multiply z1 z2)
  (let ([a (real z1)]
        [b (imag z1)]
        [c (real z2)]
        [d (imag z2)])
    (complex-num ..compute ac-bd..  ..compute bc+ad.. )))

在Scheme中将两个复数相乘

2 个答案: