rbzima said:I'm assuming that they simply are asking for a graphic representation of this problem. In which case simply draw the imaginary part of z, which is simply a perpendicular line from the real axis to the point z, and z* would simply be the perpendicular line from the real axis in quadrant 4 of the Cartesian coordinate system.
buzzmath said:Can anyone give me some advice on how to solve this problem?
in the reflection principle if f(x) is pure imaginary then the conjugate of f(z)=-f(z*) where z* is the complex conjugate of z.
Any advice on where to start?
thanks
Dick said:? I have no idea what that is supposed to mean. The problem is, in fact, about extending the domain of definition of an analytic function. rbzima, aren't you supposed to be working on group theory?
racland said:The problem states:
Find the Radius of Convergence of the following Power Series:
(a) ∑ as n goes from zero to infinity of Z^n!
(b) ∑ as N goes from zero to infinity of (n + 2^n)Z^n
For (a) I think the radius of convergence is 1 but I'm a bit unsure of that...
Complex analysis is a branch of mathematics that deals with the study of complex numbers, which are numbers that have both a real and imaginary component. It is important because it is used to solve problems in many areas of science, engineering, and technology, such as in electromagnetism, fluid dynamics, and quantum mechanics.
To solve complex analysis problems, it is important to have a good understanding of the basic concepts and techniques. Start by reviewing the properties of complex numbers, such as addition, subtraction, multiplication, and division. Then, familiarize yourself with the different ways to represent complex numbers, such as in Cartesian and polar forms. Next, learn how to apply these concepts to solve problems by practicing with various types of problems and seeking guidance from textbooks or online resources.
Some common techniques used in solving complex analysis problems include using the properties of complex numbers, such as the distributive property and the laws of exponents, to simplify expressions. Another technique is to use the geometric interpretation of complex numbers, where they can be represented as points on a complex plane, to solve problems involving geometric figures. Additionally, using calculus techniques, such as differentiation and integration, can also be helpful in solving complex analysis problems.
To check if your solution to a complex analysis problem is correct, you can use various methods such as substitution, graphing, or plugging in values to verify if the solution satisfies the given problem. Additionally, you can also compare your solution to the answers provided in the back of a textbook or seek help from a tutor or instructor.
Yes, when faced with more challenging complex analysis problems, it can be helpful to break them down into smaller, more manageable parts. Also, make sure to carefully read and understand the problem before attempting to solve it. If you get stuck, try approaching the problem from a different angle or seeking help from others. Practice and perseverance are key in successfully solving challenging complex analysis problems.