First, the definition of yoke function
* * * Yoke function means that for a complex number z=a+bi, the sign of imaginary part bi will change under the operation of * * * Yoke function. * * * The yoke function is represented by the symbol "z*", which can be expressed as z*=a-bi. Where a is the real part of the complex number z and b is the imaginary part of the complex number z. * * * yoke result of the York function is still a complex number.
Second, the essence of * * * yoke function
The basic algorithm of 1 * * Yoke function: (z 1+z2)*=z 1*+z2*, (z 1-z2)*=z 1*-z2*, (z65438+. That is, the * * * yokes of addition, subtraction, multiplication and division of two complex numbers are equal to the corresponding complex numbers, and the corresponding operations are carried out after taking the * * * yokes respectively.
2. The relationship between the square of the * * yoke function and the module length: | z | 2 = z * z *. That is to say, the square of the module length of the complex number z is equal to the product of the complex number z and its yoke.
3. The * * * yoke of the * * yoke function is equal to the original complex number: (z *) * = z That is, the * * * yoke function is operated twice on a complex number, and the result is equal to the original complex number.
4. Relationship between * * * Yoke Function and Real Part and Imaginary Part: If z=a+bi, then z*=a-bi. * * * yoke York function changes the sign of the imaginary part of a complex number.
Third, the application of * * * yoke function
1. * * Yoke property of complex variable function: In complex variable function, if complex * * * Yoke function appears in the expression of the function, it can be simplified by using the property of * * * Yoke function.
2. Separation of real part and imaginary part of complex number: By calculating the sum and difference of complex number and its yoke, the separation value of real part and imaginary part of complex number can be obtained, which is of great significance in some applications.
3. Square of complex modulus length: The square of complex modulus length can be obtained by calculating the product of complex number and its yoke, which is often used to calculate complex modulus length and judge whether complex number is a real number.
Four. * * * Example of Yoke Function
1. Example 1: For the complex number z=3+4i, its * * * yoke function is z*=3-4i.
2. Example 2: For complex number z=-2i, its * * * yoke function is z*=2i.
3. Example 3: For complex number z=5, its * * * yoke function is z*=5.
Verb (abbreviation of verb) abstract
* * * Yoke function operates on a complex number and takes the reciprocal of its imaginary part. It has some basic properties, such as the basic algorithm of * * * yoke function, the relationship between square and module length, etc. * * * Yoke function plays an important role in complex variable function, which can simplify and calculate the expression of complex variable function. At the same time, the yoke function can also be used to calculate the deviation between the real part and the imaginary part of a complex number and judge whether the complex number is a real number. Through examples, we can better understand and apply the * * * yoke function.