Research On Complex Number In High School Mathematics Competition

With the introduction of the plan for strengthening basic disciplines,the status of basic disciplines is becoming more and more important.As the basis of science,the mathematics subject has a pivotal position.The knowledge of complex numbers is one of the important contents in the teaching of high school mathematics.Compared with foreign textbooks,the requirements for the knowledge of complex numbers in Chinese textbooks are relatively low,while the requirements for the knowledge of complex numbers in high school mathematics competitions,as an important channel to select and cultivate the cutting-edge talents in mathematics,are increased significantly.The purpose of this paper is to study the knowledge of complex numbers in high school mathematics competitions,enrich the content of mathematics competitions and understand the properties of complex numbers and the applications of complex numbers more comprehensively.This paper uses literature analysis and statistical research method to collect all the questions about complex numbers in high school mathematics league,International Mathematical Olympics,and Chinese Mathematical Olympics and classifies the collected questions into the use of basic knowledge of complex numbers,the use of complex numbers in trigonometric problems,the use of complex numbers in algebraic problems,and the use of complex numbers in geometric problems.According to the comprehensive difficulty analysis model based on AHP theory,the test questions were analyzed from the following factors:background factors,whether or not they contained parameters,arithmetic level,reasoning ability,knowledge content,thinking direction,and cognitive level.According to Polya's how to solve table,the test questions were analyzed in four steps: clarifying the problem,formulating a plan,realizing the plan,and reviewing the test questions.According to the results of statistical analysis,it was found that(1)the comprehensive difficulty of the questions increased sequentially from the use of basic knowledge of complex numbers,the use of complex numbers in trigonometric problems,the use of complex numbers in algebraic problems to the use of complex numbers in geometric problems.(2)Two important factors affecting the difficulty of complex number-related test questions are knowledge content and background factors.(3)When complex number-related knowledge is tested in high school competitions,the greatest proportion of the test is devoted to the knowledge points related to complex numbers and geometry,followed by the test on the use of complex numbers in algebraic problems.The article concludes with a summary and suggestions based on the conclusions of the analysis,analyzes the inadequacies of the study,and hopes that this study can be applied practically.