Analytic Function Homework: Exp[(z^3+1)/(z-1)]

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In summary, the question is asking to determine the largest subset of complex numbers on which the function exp[(z^3+1)/(z-1)] is analytic. The author is unsure of the meaning of "analytic" and is seeking help. They are directed to look up the definition in their textbook and to consider where the derivative of the function is defined and undefined.
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Fairy111
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Homework Statement



Determine the largest subset of C (complex numbers) on which the following function is analytic.

Homework Equations



exp[(z^3+1)/(z-1)]

The Attempt at a Solution



I don't really understand what analytic means, and am having trouble starting this question.
 
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  • #2
Then you had better look up "analytic" in your textbook!
 
  • #3
i know what it means, as in the definition etc

im just not sure how to go about finding the largest subset.
 
  • #4
could someone please give me some help on this question, as i really don't understand it.
 
  • #5
Where is the derivative of the function defined? Where is it undefined?
 

1. What is an analytic function?

An analytic function is a complex-valued function that is defined and differentiable at every point in its domain. This means that it can be represented by a power series expansion and has a derivative at every point in its domain.

2. How do you find the domain of an analytic function?

In order for a function to be analytic, it must be defined and differentiable at every point in its domain. To find the domain, you can look for any values of the independent variable that would make the function undefined, such as dividing by zero or taking the square root of a negative number.

3. What is the purpose of studying analytic functions?

Analytic functions have many practical applications in mathematics, physics, and engineering. They are used to model and analyze complex systems, and they have many properties that make them useful for solving differential equations and other problems.

4. How do you find the derivative of an analytic function?

The derivative of an analytic function can be found using the rules of complex differentiation, which involve taking the limit of the difference quotient as the change in the independent variable approaches zero. The derivative of an analytic function is also an analytic function.

5. How do you solve problems involving analytic functions?

To solve problems involving analytic functions, you can use techniques such as integration, differentiation, and finding zeros and poles. You can also use the properties of analytic functions, such as the Cauchy-Riemann equations and the Cauchy integral formula, to simplify and solve problems.

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