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十六世纪二十至五十年代,意大利波龙尼亚大学数学家非尔洛、邦别利及米兰医生卡尔达诺等人在研究三次方程一般解法的过程中,出于扩充实数的需要引进了复数。但当时只是作为“数学正确运算的结果”(恩格斯语)形式地引进的。它的实际意义在长达近三百年的过程中人们了解得并不够清楚,“虚数”这一名词本身就反映了这一点。直到十九世纪上半叶,经阿尔干(1806)、高斯(1831)等人的工作,把复数看做坐标平面上的一个点之后,才被真正弄清楚了,尽管仍然采用“虚数”这一名词,但已认识到完全没有“虚”的意思了。
From the 20th to the fifties of the 20th century, the mathematicians of the University of Bologna of Italy, Filello, Bonbily, and Milano Caldano, etc., introduced the general solution to the cubic equation and introduced it for the expansion of real numbers. Plurals. However, it was only introduced as a “result of mathematical correct calculations” (Engels). Its practical significance was not clearly understood in the course of nearly three hundred years. The term “imaginary number” itself reflects this. Until the first half of the 19th century, after the work of Argan (1806), Gauss (1831), etc., took the complex number as a point on the coordinate plane, it was only really clear, although the “imaginary number” was still used. A noun, but it is recognized that there is no meaning of “virtuality.”