培养学生具有正确、迅速的运算能力,是中学数学教学的重要目的之一。运算的合理化技能是正确、迅速运算的保证。下面以全日制十年制学校高中数学课本第三册中的若干练习题为例,谈谈培养学生复数运算的几种解题技能。一关于复数-1/2+3~(1/2)i/2的应用技能课本中把它记作ω =-1/2+3~(1/2)i/2,它的共轭虚数为ω=-1/2-3~(1/2)i/2,这一对共轭虚数的特点有: 1.ω~3=1,ω~3=1,即1的立方根是1,ω、ω; 2.ω·ω=1; 3.ω~2=ω,ω~2=ω; 4.1+ω+ω~2=0,1+ω~2+ω~2=0, 1+ω+ω~2=0,1+ω+ω=0。其应用举例如下: 例1 (课本P88,1(4)题), Cultivating students with the correct and rapid computing skills is one of the important goals of mathematics teaching in middle school. The rationalization of computational skills is a guarantee of correct and rapid calculations. The following is an example of some of the exercises in the third volume of the high school mathematics textbook for full-time 10-year high school students. An application skill for the complex number -1/2+3~(1/2)i/2 is written in the textbook as ω = -1/2+3~(1/2)i/2 and its conjugate imaginary number For ω=−1/2−3~(1/2)i/2, the characteristics of this pair of conjugate imaginary numbers are: 1.ω~3=1, ω~3=1, that is, the cube root of 1 is 1. ω, ω; 2.ω·ω=1; 3.ω~2=ω,ω~2=ω; 4.1+ω+ω~2=0,1+ω~2+ω~2=0, 1+ ω+ω~2=0, 1+ω+ω=0. Examples of applications are as follows: Example 1 (textbook P88, 1(4)),