CAJ | 학술논문

虚数是为了解决数学本身的问题而引入的，人们把虚数当做数来使用源于三次方程而非二次方程．在相当长的时间里，人们对负数的平方根究竟是不是数持怀疑态度，甚至有所抵制．在几何学思想一统天下的时代，如果虚数没有对应的几何意义，那么它在数学中就没有立足之地．经过几代数学家近三百年的争论与求索，1831年高斯详尽而系统地表述了平面笛卡儿几何与复数域的等价性，揭示了复平面与复数集的一一对应关系．
허수시위료해결수학본신적문제이인입적，인문파허수당주수래사용원우삼차방정이비이차방정．재상당장적시간리，인문대부수적평방근구경시불시수지부의태도，심지유소저제．재궤하학사상일통천하적시대，여과허수몰유대응적궤하의의，나요타재수학중취몰유립족지지．경과궤대수학가근삼백년적쟁론여구색，1831년고사상진이계통지표술료평면적잡인궤하여복수역적등개성，게시료복평면여복수집적일일대응관계．
Imaginary numbers have been conceived to solve mathematical problems, as a number of mathematicians are from the cubic equation rather than the quadratic equation. For a long time, such numbers were poorly understood and regarded by some as fictitious or useless 1, or even resist. Geometry dominate the world in the era of thinking, if there is no corresponding geometric meaning, it has no place in mathematics. After several generations of mathemati- cians, nearly three hundred years of debate and explorations, in 1831 Gauss detailed and systematic formulation of the Cartesian plane geometry and complex field of equivalence, and reveals the geometric significance of complex numbers as points in a plane.