# Complex analysis

buzzmath
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

buzzmath
sorry I posted in the wrong forum

Homework Helper
I assume 'f(x) pure imaginary' means pure imaginary along the real axis. In which case you might want to consider g(z)=i*f(x). What kind of a function is g on the real axis?

rbzima
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.

Homework Helper
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.

? 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?

Wiemster
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

How is this a problem (I see no (implicit) question mark)?

Homework Helper
He's stating a variant of the Schwarz reflection principle. And trying to prove it.

rbzima
? 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?

LOL - This caught my attention, but I managed to finish my group theory stuff. Forgive me if I was wrong, but you don't really have anything to "solve" using what you stated. If f(x) is pure imaginary, it will exist on the imaginary axis, and it's conjugate will then exist on the imaginary axis as well. Maybe I'm just reading the question wrong.

Homework Helper
Look up the reflection principle and then read the question again. He wrote f(x) is pure imaginary. He didn't write that f(z) is. This is intended as f(x) is imaginary when x is real. Purely imaginary analytic functions are pretty trivial.

racland
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...