* * * Yoke complex number refers to two complex numbers with the same real part and opposite imaginary part. For example, the * * * yoke complex of a+bi is a-bi.
Polynomial equation refers to an algebraic equation in which the highest power of one or more variables is 1. For example, AX 2+BX+C = 0 is a quadratic polynomial equation.
Now discuss the relationship between the root formula of * * * yoke complex equation and polynomial equation.
First of all, we can express a polynomial equation as the product of two polynomial equations, one of which contains only real terms and the other contains only imaginary terms. For example, for the quadratic polynomial equation ax 2+bx+c = 0, we can express it as (ax+b)*(x+sqrt(c/a))=0. Here sqrt(c/a) is the square root of c/a, which can be a real number or an imaginary number.
Next, we consider the complex form of this quadratic polynomial equation. For quadratic polynomial equation AX 2+BX+C = 0, its * * * yoke complex is AX 2+BX+C = 0. We can see that these two equations are actually the same.
Now, let's discuss how to solve these two equations. For polynomial equations with real terms, we can use the properties of real roots to solve them. For example, a polynomial with real terms has two unequal real roots, then these two roots are the real roots of the original equation. Similarly, if the polynomial of the real term has two equal real roots, then these two roots are the repeated real roots of the original equation.
For polynomial equations with imaginary terms, we can use the properties of imaginary roots to solve them. For example, if the polynomial of the imaginary term has an imaginary root that is not equal to zero, then this root is the imaginary root of the original equation. Similarly, if the polynomial of the imaginary term has no imaginary root that is not equal to zero, the original equation may have no imaginary root.
In this way, we can decompose a complex yoke equation into two polynomial equations and solve them separately. Finally, we combine the real root and imaginary root to get the solution of the original yoke complex equation.
In a word, the root formula of * * * yoke complex equation is closely related to polynomial equation. The complex equation of * * * yoke is decomposed into two polynomial equations, and the solution of the original complex equation of * * * yoke can be obtained by solving them respectively. This method is very useful in solving practical problems, especially in dealing with mathematical problems involving complex numbers.