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1837年,英国数字家哈蜜顿(Hamilton)通过研究发现复数a+bi不是2+3意义上的一个真正的和,加号的使用只是历史的偶然,而bi不能加到a上去,复数a十bi只不过是实数的有序偶(a,b)。高斯(Gauss)给出复数的几何表示之后,数学家们认识到复数能用来研究且可以表示平面上的向量,然而,复数的利用是受限制的,如,设几个力作用在一物体上,这些力不一定在同一个平面上。代数上处理这些力需要复数的一个三维类似物,我们能用点的通常的笛卡尔坐标(x,y,z)来代表原点到该点的向量,但不存在包括加法、减法、乘法和除法在内且满足结合律、
In 1837, the British digitalist Hamilton found through research that the plural a + bi is not a true sum in the sense of 2 + 3. The use of a plus sign is only a historical accident and bi can not be added to a. The complex numbers a Ten bi is just a real ordered pair (a, b). After Gauss gives the geometrical representation of complex numbers, mathematicians realize that complex numbers can be used for research and can represent vectors on planes. However, the use of complex numbers is limited. For example, suppose several forces act on an object These forces are not necessarily in the same plane. Algebraic processing of these forces requires a complex three-dimensional analogue. We can represent the vector from the origin to the point using the usual Cartesian coordinates of the point (x, y, z) but there are no additions including addition, subtraction, multiplication and division And meet the law of combination,