An example using Cauchy's theorem
Not what you're looking for?
Let f be entire. Evaluate the integral from zero to 2 pi of f(z_0+re^(i theta)) e^(ik theta), where z_0 is a constant and k is a constant greater than or equal to 1.
Purchase this Solution
Solution Summary
Cauchy's theorem tells us that the integral of an entire function around a closed contour is zero. Attached is a 1/2 page solution written in Word with equations in Mathtype illustrating the use of this theorem. It also illustrates how substitution is often used to turn an integral into a contour integral to which the theorem may be applied.
Solution Preview
Solution is attached.
It sounds like you've done it right, and probably by exactly the method I'm about to show you!.
It is not explicitly stated, but I am assuming . (if , then and the question can be solved by integrating ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Probability Quiz
Some questions on probability
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.