Key points of complex number knowledge: Complex number is an important content of high school algebra, accounting for about 8%- 10% of the college entrance examination questions. Generally, a basic question and an intermediate question are produced, which often combine knowledge of trigonometry, analytic geometry, equations, inequalities and so on. The main contents of this chapter are the concept of complex number, algebra, geometry, triangle representation and complex number operation.

It is prominent in this chapter to combine the number and shape of the equation, discuss it in different domains and transform it into equivalent mathematical ideas and methods. Complex number is the hub of algebra, trigonometry and analytic geometry knowledge, which is beneficial to broaden students' thinking and improve their ability to solve comprehensive exercises. The operation of numbers and formulas and the solution of equations, equations and inequalities are the basic skills to learn this chapter well. The consciousness of simplifying operation should also be further strengthened.

Difficulties in complex numbers

Operation of (1) complex vector representation. Some students can't master the vector representation of complex numbers well, and it is difficult to master the geometric meaning of vector operation flexibly. We should carefully understand the geometric meaning of complex vector operation and prove it flexibly.

(2) The power sum root of complex triangle form. Some students know the algorithm, but they have some difficulties in using it flexibly, especially the square root operation, so they should be trained carefully.

(3) Solving the complex principal value.

(4) Using the geometric meaning of complex numbers to solve problems flexibly. Complex numbers can be represented by vectors, and the modulus and angle of complex numbers have geometric significance. It is difficult to understand and use them, so we should understand them carefully.

Key points in complex numbers

(1) Understand the concept of complex number and find out the difference between real number, imaginary number and pure imaginary number.

(2) Master the three representations of complex numbers and their mutual transformation, and accurately find the modulus and angle of complex numbers. There are three representations of complex numbers: algebra, vector and triangle. Especially, the mutual transformation between algebraic form and triangular form, and finding the modulus and angle of complex numbers are often used in solving specific problems, which is a key content.

(3) Various operations of three representations of complex numbers, among which we pay attention to the related properties of complex numbers and modules. Complex number operation is the main content, and mastering various forms of complex number operation, especially the geometric meaning of complex number operation is the key content.

(4) Solving quadratic equation and binomial equation in complex set.