论文部分内容阅读
虚数在过去一般中学教科书里面是名副其实的『虚』数。编者告诉学生说,以前我说过,负数没有平方根,现在请大家承认 i 的平方等于于—(?).于是学生仿照例题计算复数的加减乘除,计算含有虚数的复杂的算式,求方程式的虚根,却完全不知道计算的是些什么东西,也不知道学了这种计算会有什么用处。另一方面,大学教科书形式地界说复数为所谓“实数偶”。两个实数偶怎样相加呢?定义是(a,b)+(c,d)=(a+c,b+d).这似乎有些道理,比方,a 斤米 b 斤豆加 c 斤米 d 斤豆等于 a+c 斤米 b+d 斤豆。但两个实数偶怎样相乘呢?定义是(a,b)(c,d)=(ac-bd,ad+bc).这样界说乘法,理由是什么呢?
The imaginary number is literally the “imaginary” number in the general school textbooks of the past. The editor told the students that I had said before that the negative number has no square root. Now, please recognize that the square of i is equal to -(?). So the student simulates the addition, subtraction, multiplication and division of complex numbers according to the example, and calculates the complex formula containing the imaginary number. The imaginary roots do not know what the calculations are, nor do they know the usefulness of learning such calculations. On the other hand, university textbooks formally define the plural as the so-called “real number couple.” How do the two real numbers add? The definition is (a,b)+(c,d)=(a+c,b+d). This seems a bit plausible, for example, a kg of rice b plus beans plus c kg of rice d Pound beans equal a+c pounds meters b+d pound beans. But how do the two real numbers are multiplied? The definition is (a,b)(c,d)=(ac-bd,ad+bc). What is the reason for this definition of multiplication?