The Geometric Features And Practical Research Of Complex Operation

As is known to all, with the development of the times, Modern mathematics teaching in middle school has changed significantly. Despite the unchanged teaching topics in the realm of algebra, as the consequence of the national curriculum reform, there are a lot of modifications in teaching content, teaching materials and teaching methods. The alteration in the teaching of the complex number is a good example.As a significant part of number system which is the basis of mathematics, it is of importance and necessity. With the development of complex number theory, disciplines such as complex function theory, analytic number theory,relativity and quantum mechanics develop correspondingly. This indicates that the complex number is an indispensable teaching content.And that’s why in the mathematics curriculum reforms of many foreign countries such as Russia, France, Britain, Japan and Singapore, more importance and higher demand are attached to the teaching of the complex number. Students are required to not only know the origin,development, geometric meaning and application of the complex number, but also to have a good knowledge of its geometric features and the ability to solve practical problems with it.However, the teaching requirements for the complex number since the implementation of China’s curriculum reform are getting simpler and formalistic.In this case, it is advisable to start the chapter of the complex number with its definition and significance and then probe into its geometric features of operations and finally apply it to solve some practical problems. on the basis of existing knowledge about complex number, it is necessary for students to know about the geometrical character of complex number and the simple application of the geometrical character of complex operation, which will help students find pleasure in studying complex number, have a better knowledge of of the geometric meaning and algebraic operation of complex number, and have a better understanding of complex number. This essay studies the geometrical character of complex operation in the complex plane and comes to a conclusion that if a non-zero complex number Z₁ is taken, the argument of complex number Z, the multiplication of non-zero complexnumbers Z₁ and Z2, will be the angle when Z2 is rotated counterclockwise with the argument of Z₁. Besides, this essay also shows that when the real axis and an imaginary number form an angle of θ（0°<θ<180°）, the argument α ofZ =Z₁·i is the same as that of complex conjugate of Z₁. And the algorithms of operation is given from a rotation angle.