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课题复平面上点的轨迹问题目的使学生会用参数法解决简单的复平面上点的轨迹问题,并通过本节课的教学提高学生综合分析能力。课型习题课。教法讲练结合,启发式过程:例1 已知复平面上A、B两点表示的复数分别是1+i和1-i。表示复数z的动点N在线段AB上移动,求复数z~2所对应的点M的轨迹。轨迹的探求:(由老师引导学生解答下列问题) (1)如图1当N点分别落在A、B、E三点上,相应的M点会分别落在哪些地方? 答:利用公式|z~2 |=|z|~2,和argz~2=2argz(或者argz~2=2argz-2π)可知点M依次落在图1中的C、D、E上。
The purpose of the trajectory problem on the complex plane of the subject is to enable students to use the parametric method to solve simple trajectory problems on the complex plane, and to improve the students’ comprehensive analysis ability through the teaching of this lesson. Class exercises. Teaching method combines training and heuristic process: Example 1 It is known that the complex numbers represented by two points A and B on the complex plane are 1+i and 1-i, respectively. The moving point N representing the complex z is moved on the line AB to find the locus of the point M corresponding to the complex z2. The search for the trajectory: (The teacher guides students to answer the following questions) (1) As shown in Figure 1, when the N points respectively fall on the three points A, B, and E, where will the corresponding M points fall? z~2 |=|z|~2, and argz~2=2argz (or argz~2=2argz-2[pi]) It can be seen that points M successively fall on C, D, E in FIG.