1. addition rule
The addition rule of complex numbers: let z 1=a+bi and z2=c+di be any two complex numbers. The real part of sum is the sum of the original two complex real parts, and its imaginary part is the sum of the original two imaginary parts. The sum of two complex numbers or a complex number. that is
2. Law of multiplication
Complex multiplication rule: two complex numbers are multiplied, similar to two polynomials. In the result, i2=-1, and the real part and imaginary part are merged respectively. The product of two complex numbers is still a complex number. that is
3. Division rule
Definition of complex division: satisfying
plural
Divide the complex number a+bi by the complex number c+di.
Operation method: the numerator and denominator are multiplied by the * * * yoke complex number of the denominator at the same time, and then operated according to the multiplication rule.
that is
4. Basic rules
If Zn = r(cosθ+isθ), then
(k=0， 1，2，3…n- 1)
5. Operating rules
Additive commutative law: z 1+z2=z2+z 1.
Multiplicative commutative law: z 1×z2=z2×z 1.
Additive associative law: (z1+z2)+z3 = z1+(z2+z3)
The law of multiplicative association: (z1× z2 )× z3 = z1× (z2× z3)
Distribution law: z/kloc-0 /× (z2+z3) = z/kloc-0 /× z2+z/kloc-0 /× z3.
6. My Law of Power
I4n+ 1 = i, i4n+2 =- 1, i4n+3 =-i, i4n = 1 (where n∈Z).
7. Demofo Theorem
For the complex number z = r(cosθ+isθ), there exists the n power of z.
Zn=rn[cos(nθ)+isin(nθ)] (where n is a positive integer)
rule
Extended data * * * interpretation of yoke complex number
For complex numbers
Call it a complex number.
=a-bi is the * * * yoke complex number of z, that is, two complex numbers with equal real parts and opposite imaginary parts are conjugate complex numbers. The * * * yoke of the complex number z is written as
nature
By definition, if
(a, b∈R), then
=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 points representing the complex number of two yokes are symmetrical about X, which is the origin of the word "* * * yoke"-two cows pull the plow in parallel with a beam on their shoulders, which is called "yoke". If x+yi is represented by z, then adding a "one" above the word z is x-yi, and vice versa.
* * * yoke complex numbers have some interesting properties:
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