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Complex number algorithm
The operation of negative numbers includes the law of addition, the law of multiplication, the law of division, the law of square root, the law of operation, the law of power of I and so on. The specific operation method is as follows:

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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