Method for solving complex equations f(z)=0

In summary, The conversation discusses different methods for solving complex equations of one complex variable and mentions Newton's method, bisection method, and Ridder's Method. It is noted that choosing the best method may depend on the specific problem at hand.
  • #1
liviuct
2
0
Hey! Does anyone know any good method for solving complex equations of one complex variable? I found over the internet that I could use Newton's method, and I tried it for a common function, and it worked. Anyway, I'm not very pleased of Newton's method because of the use of the first aproximation value. Also it does not return all the solutions. I need it for calculating some resonances energies for my Bachelor Thesis in Quantum Mechanics.
I also tried methods for real functions (in order to integrate the Schrodinger Equations and obtaining the eigenvalues), like bisection method or Ridder's Method. They worked just fine.

Thank you.
 
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  • #2
For most equations you need a guess as an approximate solution or a bracket. Which method works best tends to be problem specific.
 

What is the Method for solving complex equations f(z)=0?

The Method for solving complex equations f(z)=0 is a mathematical process used to find the values of z that satisfy the given equation. It involves manipulating the equation and using algebraic and numerical techniques to find the solutions.

Why is it important to solve complex equations?

Solving complex equations is important in various fields of science, such as physics, engineering, and economics. It allows us to understand and predict the behavior of systems and make informed decisions based on the solutions obtained.

What are some common techniques used in solving complex equations?

Some common techniques used in solving complex equations include factoring, completing the square, and using the quadratic formula. Other methods such as substitution, elimination, and graphing can also be used depending on the complexity of the equation.

Can complex equations have multiple solutions?

Yes, complex equations can have multiple solutions. In fact, some equations may have an infinite number of solutions. This is because complex numbers have both a real and imaginary part, allowing for more possible solutions compared to real numbers.

Are there any limitations to the Method for solving complex equations f(z)=0?

While the Method for solving complex equations f(z)=0 is a powerful tool, it does have some limitations. It may not work for all types of equations, especially those with multiple variables or non-polynomial functions. In some cases, numerical methods may need to be used to approximate the solutions.

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