Complex number refers to the number a+bi which can be written in the following form, where A and B are real numbers and I is imaginary unit (i.e.-1 root). Cardin, an Italian scholar in Milan, was first introduced in16th century. Through the work of D'Alembert, De Moivre, Euler and Gauss, this concept was gradually accepted by mathematicians. There are many ways to express complex numbers, such as vector representation, triangle representation, exponential representation and so on. It satisfies the properties of four operations. It is the most basic object and tool in complex variable function theory, analytic number theory, Fourier analysis, fractal, fluid mechanics, relativity, quantum mechanics and other disciplines. The number set is extended to the real number range, but some operations are still impossible. For example, the univariate quadratic equation with discriminant less than 0 still has no solution, so the number set is expanded again to reach the complex range. Definition: A number in the form of z=a+bi is called a complex number, where I is defined as an imaginary unit, and I 2 = I * I =-1(A and B are arbitrary real numbers). We call the real number A in the complex number z=a+bi the real part of the imaginary number Z, and we call it Rez=a, and the real number B the imaginary part of the imaginary number Z (IMA). When a=0 and b≠0 and z=bi, we call it pure imaginary number. Definition: For the complex number z=a+bi, the complex number z' = a-bi is called * * * yoke complex number definition: the value of the positive square root of the sum of the squares of the real part and imaginary part of a complex number is called the modulus of the complex number, which is called ∣z∣, that is, for the complex number z=a+bi, its modulus ∣ z ∣ = ∣. The set of proper subset complex numbers with r as c is [edit this paragraph]. Let the four operations of complex numbers be z 1 = a+bi and z2 = c+di, then there are the following rules for linear operation addition and subtraction: (a+bi) (c+di) = (a c)+(b d) I number multiplication: c * (a+bi). 6? 1 (c+di) = (ac-bd)+(bc+ad) i，(a+bi)÷(c+di)=[(AC+BD)/(C2+D2)]+[(BC-ad)/