One of our review problems for my complex analysis final is the following:     Show that $e^z=z$ has infinitely many solutions in $\mathbb{C}$.   I've seen a few solutions online, but none of them have used material that was covered in our introductory complex analysis course. Would anyone be able to provide a simple solution?  I'm trying to think of ways to invoke bounding in some way but I can't seem to come up with anything.
(p.236)  has a proof that the equation $e^z-z=0$ has infinitely many complex solutions:    I'm curious if there are any particularly elegant ways to see this, other than that given in the text.
Anthology series with suspended animation and a galaxy-wide empire? Why no ooVoo on ubuntu? The only reason I ever boot into Windows (7) is to use the popular video chat software ooVoo (). It's useless under Wine and there seems to be no way to run it in Ubuntu except for some proprietary tools. Does anyone have any information on some alternatives to running it with Wine? Rank of a Matrix Sum I have $3\times3$ matrices such that S=A+B. I know there is an inequality connecting rank of the matrices A, B and its sum S. Could you write down that here? It will be a great help for me.  Means equation  or inequality connecting rank(S), rank(A) and rank(B). What is wrong with the De Broglie–Bohm theory a.k.a "Causal Interpretation" of quantum theory? Possible Duplicate:          I've heard of De Broglie–Bohm theory a.k.a causal interpretation of quantum theory. The predictions match accurately with with the nondeterministic quantum theory.  As a philosophy buff this one seems just like the classical universe. No funny new-age religion style gimmicks.  So why don't people use this interpretation instead of the Copenhagen "magic" interpretation?  P.S. I'm not an expert. I possess only superficial knowledge of quantum physics. What's the 1 inch square knob sticking out of the wall? How to stop "Monkey Test" and "Time Service" apps When I long-press the "home" button to close all apps, there is an app named "time service" with android symbol and another named "monkey test" that are always open.   How to stop this? How to re-enable tray icons for applications in Ubuntu? Flattening a shallow list in Python I've got this one file, favicon.ico. It's actually a large group of nested files, but purely for example, just this one.  If I do cp favicon.ico favicon2.ico, Apache can read the second one just fine.  If I do mv favicon.ico favicon3.ico, Apache throws a 403 on favicon3.ico.  If I su apache, I can read the file as apache.  stat says both files are identical, except for the inode number.  Is there some hidden flag somewhere or something that I'm missing? I've never seen anything like this.  error_log says (13)Permission denied: access to /favicon3.ico denied How do I install MATLAB via the ISO? How do I connect to a WPA wifi network using the command line? So basically, I'd like to use iwconfig to connect to my wifi network when I'm not inside X. But I just don't see a way to do it in the man page. Any idea? Is there a standard idiom for comparing version numbers?  I can't just use a straight String compareTo because I don't know yet what the maximum number of point releases there will be.  I need to compare the versions and have the following hold true:  1.0 &lt; 1.1 1.0.1 &lt; 1.1 1.9 &lt; 1.10 How to search for list of papers citing both papers A and B? For given papers A and B, I would like to search for all papers that cite both A and B. I guess one can generalize to papers {A,B,C,...} and find all papers that cite all of them.   A quick Google Scholar and Web of Science search revealed nothing. Google Scholar has a "cite=..." thing in the URL, which I messed with a bit to no avail. Intuitive Bernoulli numbers Custom cursor in WPF? I want to use an image or icon as a custom cursor in WPF app. What's the best way to do it? There are many times when I curse the autocorrection mechanism for changing what I typed, but overall, much of the corrections are welcome so I don't really want to disable it. I do want to have it do it's work but alert me when it makes each change so I don't have to proofread everything or focus with perfect attention to the screen to see the momentary red and/or blue underlining that alerts me to the machine override.  I would love a way to turn on an audible beep (customizable of course) so that I also get a warning each time my typing gets corrected (and only when autocorrection occurs). Natural examples of deformation retracts that are not strong deformation retracts The question  asks for examples of deformation retracts which are not strong deformation retracts. A comment is given refering the asker to Exercise 0.6 in Hatcher. (The description of this space also appears in , which is about this very same exercise.)  This space, however, seems to be constructed specifically for this purpose.     Are there any naturally occurring (by which I mean not constructed specifically for this purpose, arising in some other way) spaces that are deformation retracts but not strong deformation retracts?   The main reason for asking is that it doesn't seem very likely to me that one would stumble upon such a space at random, so I don't know what to watch out for. One can never be too careful. Can someone help me figure out the big-O for the recurrence relation $T(n) = T(n^{1/2}) + 1$?  I didn't think the master theorem would work since it requires $T(n) = T(n/b)$... to have $b$ as a constant. I was wondering if anyone could shed some light on a method to approach this problem? (not looking for a solution) Chatroom owners can star their own messages I was able to star my own message by pinning it and unpinning it.  Pinning a message adds a star, even to your own messages, but when the pin is removed, the star remains. Photons have no mass but they can push things, as evidenced by .   Can photons push the source which is emitting them? If yes, will a more intense flashlight accelerate me more? Does the wavelength of the light matter? Is this practical for space propulsion? Doesn't it defy the law of momentum conservation?  Note: As John Rennie mentioned, all in all the wavelength doesn't matter, but for a more accurate answer regarding that, see the comments in  .  Related Wikipedia articles: ,