# Homework Help: Complex function

1. Aug 30, 2011

### Cosmossos

f(z) is analytic and not equal to zero in the unit circle (|z|<=1) . we also know that |f(z)|=|e^z| for |z|=1. find f(z)

How should i approch to this question? I know that on inside the boundry it can't get the maximum nor the minimum .. but it doesn't help at all. i have no idea what to do.

Last edited: Aug 30, 2011
2. Aug 30, 2011

### HallsofIvy

Does the question imply that there is a unique answer? It is obvious that the function $f(z)= e^z$ itself satisfies all of those properties,

3. Aug 30, 2011

### Cosmossos

no, but I'm asked to find it, so I think i should do more than that

4. Aug 30, 2011

### jackmell

Jesus dude, you kinda' antagonizing huh? I mean you got a flat tire, I say, "hey, here's one that's not flat that'll fit, use it," and you say, "oh no, that one won't work." So I say, "dude, it's the same diameter, same lugs, and best of all, it's ain't flat." Then you say, . . . ok, I'll stop being anoying.

5. Aug 30, 2011

### BruceW

The question is written in a way that implies that the answer is not just ez. But maybe the question is just worded badly.

6. Aug 30, 2011

### Cosmossos

Huh? the simple answer isn't gonna work here and it is like giving the trivial solution for a set of equations . This question isn't a stupid college question but some levels above that and needed a little bit more then just stating the answer . jackmell , next time, think before you shoot...

By the way, this isn't the complete answer ... so my friend, I'm glad I didn't took you tire...

And for the one who actually try to answer my question, thank you very much and I didn't meant to insult you in any way.

7. Aug 30, 2011

### Cosmossos

You are correct

8. Aug 30, 2011

### jackmell

It's a teachable moment. Sometimes in math, the obvious solution is in fact the answer. Don't try and make it more complicated than it is. Final exam, you ask me that question, I'm going with e^x. Bingo-bango, wait a while so I'm not the first one to leave the class then I'm outta there.

9. Aug 30, 2011

### Cosmossos

In that case you got 5 out of 20. enjoy

10. Aug 30, 2011

### jackmell

I don't think there is a single teacher teaching Complex Analysis in the entire world that would disagree with me. Well, maybe not the smart-elic stuf. Mostly just playing around.

Last edited: Aug 30, 2011
11. Aug 30, 2011

### BruceW

You sound like you have some idea of what the actual answer is..?
If I had to guess, I would say ez was a correct answer, despite the strangely-worded question.

12. Aug 30, 2011

### HallsofIvy

Why not? That was why I asked "Does the question imply that there is a unique answer?" The question said " find f(z)" which seems to me to imply that there is a unique solution- in which case it would have to be $e^z$.

13. Aug 30, 2011

### BruceW

There is another possibility for f(z) that I can think of.

14. Aug 30, 2011

### Cosmossos

Do you mind sharing?

15. Aug 30, 2011

### BruceW

Does it matter? Its another obvious one. And you said "but I'm asked to find it, so I think i should do more than that ... the simple answer isn't gonna work here and it is like giving the trivial solution for a set of equations ... By the way, this isn't the complete answer " So I'm guessing you've been told that its not just an easy answer?

16. Aug 30, 2011

### Cosmossos

come on ... The level of the course is more than that. believe me , I KNOW.
No one would give us this question if that was the answer

17. Aug 30, 2011

### BruceW

If it is not an easy answer, then I can't for the life of me think what the answer is. Sorry I haven't really been able to help

18. Aug 31, 2011

### Cosmossos

Thank you everyone for try to help me!