We call the real number A in the complex number z=a+bi the real part of the complex number Z, and write it as REZ = A.
The real number b is called the imaginary part of the complex number z, and is recorded as imz = B.
It is known that when b=0 and z=a, then a complex number becomes a real number.
When a=0 and b≠0 and z=bi, we call it pure imaginary 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 module of the complex number, and it is recorded as ∣z∣.
That is, for the complex number z=a+bi, its modulus ∣ z ∣ = ∣ (A 2+B 2).
The set of complex numbers is represented by C, and the set of real numbers is represented by R. Obviously, R is the proper subset of C.
The complex set is out of order, and the size order cannot be established.
Complex number of * * * yoke
Definition: For the complex number z=a+bi, call the complex number z'=a-bi the * * * yoke complex number of z, that is, the two real parts are equal, and the imaginary part (imaginary part is not equal to 0) is a conjugate complex number. The * * * yoke of the complex number z is denoted as zˊ. The representation method is to add a horizontal line above the letter Z, that is, the * * * yoke symbol. According to the definition, if z=a+bi(a, b∈R), then z = a-bi (a, b ∈ r). * * * The point corresponding to the complex number of the yoke is symmetrical about the real axis. Two complex numbers: x+yi and x-yi are called * * * yoke complex numbers. Their real parts are equal, but their imaginary parts are opposite. On the complex plane. The point representing the complex number of two yokes is symmetrical about X, which is the origin of the word "* * * yoke". Two cows pull a plow in parallel with a beam on their shoulders. This beam is called a "yoke". If X+Yi is represented by z, then adding a "1" to z is X-Yi, and vice versa. * * * yoke complex number has some interesting properties: ︱x+yi︱=︱x-yi︱ (x+yi)*(x-yi)=x? +y？ =︱x+yi︱？ =︱x-yi︱？
Four algorithms
If the complex number z 1=a+bi, z2=c+di, where a, b, c and d∈R, then z1z2 = (a+bi) (c+di) = (a+bi)+(c+di) =
Complex number addition and multiplication algorithm
z 1+z2 = z2+z 1； (z 1+z2)+z3 = z 1+(z2+z3)； z 1z 2 = z2z 1； z 1(z2z 3)=(z 1z 2)z3； z 1(z2+z3)= z 1z 2+z 1z 3
My strength
I (4n+ 1) = I, I (4n+2) =- 1, I (4n+3) =-I, I 4n = 1 (where n∈Z).
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