How to open a form from a string in C #?
Create an instance of a class from a string
The $n$ complex $n$th roots of a complex number $z$ Suppose $z$ is a nonzero complex number, so $z=re^{i\theta}$. Show that there are only $n$ distinct complex $n$-th roots, given by $r^{1/n}e^{i(2\pi k+\theta)/n}$ for $0\leq k\leq n-1$.   My proof: Let $z=re^{i\theta}\in\mathbb{C}$ and $a\in\mathbb{C}$ s.t. $a^{n}=z$. Let $a=\rho e^{i\varphi}$. Then, $a^{n}=(\rho e^{i\varphi})^{n}$. Setting $\rho^{n}e^{i\varphi n}=re^{i\theta}$ and rewriting in polar form, we get $$\rho^{n}(\cos(n\varphi)+i\sin(n\varphi))=r(\cos(θ)+i\sin(\theta)).$$ Thus $\rho^{n}=r$ $\rightarrow$ $\rho=r^{1/n}$ and $n\varphi=\theta\rightarrow\varphi=\theta/n$. Thus the roots of $a\in\mathbb{C}$ have the form $$r^{1/n}(\cos(\tfrac{\theta}{n})+i\sin(\tfrac{\theta}{n}))=r^{1/n}(\cos(\tfrac{\theta}{n}+2\pi j)+i\sin(\tfrac{\theta}{n}+2\pi j))$$ for some $j\in\mathbb{Z}$ due to the periodicity of trig functions. Then, $$r^{1/n}(\cos(\tfrac{\theta}{n}+2\pi j)+i\sin(\tfrac{\theta}{n}+2\pi j))=r^{1/n}e^{i\left(2\pi j+\tfrac{\theta}{n}\right)}=r^{1/n}e^{i(\theta+2\pi k)/n}$$ for $0\leq k\leq n-1 ,j=nk\in\mathbb{Z} $.  I feel like there could be a more concise way to put this. What to do when you find a bad link in an answer? If a link has gone stale in an answer, what is the correct way to report this in the SO universe?  e.g. Jon's first link in    I have added a comment but not found the correct link yet. Is there any way to tell Google to display the updated title instead of displaying the old blog title in search results? As a matter of optimization, a few weeks ago I modified the way the titles of my blog posts are displayed (I made a change also in the title of the blog). Then I used the Google Webmaster Tools to re-index the old pages and update titles. Immediately I could update the titles and posts appear correctly on Google.  The problem is that now the titles of posts began to appear incorrectly in the search, using the old blog title. Some posts continue to display the updated title, but many recent posts show the old title.  I've tried re-index the pages with Google Webmaster Tools, but the titles remain unchanged in the search results.  Is there any way to "force" Google to display the correct titles? rsync and symbolic links I want to backup my home directory to an external drive nightly using a cron job to execute rsync.  I am unsure of the exact behavior of rsync's symbolic link flags.   rsync's -a flag includes the -l flag (i.e. "copy symlinks as symlinks").  Does this just mean it will copy the link or that it will follow the link and copy everything in the link-to directory?  I want to avoid that because I have links to directories full of media files that would involve copying hundreds of gigabytes I don't need to back up. Fearing (but not certain) that rsync -a would copy all those media files I instead added the --no-links flag.  This does not seem to be behavior I want.  It just ignores copying any link which is problematic because I do have links I want copied (e.g. links to common header files from different project directories). Assuming #1 above (without the --no-links flag) is what I really want and it just copies the link without copying the linked-to files, will the links break when they are backed up?  For example I may rsync source directory /home/me/projects/misc to /media/extdrive/backup/home/me/projects/misc.  In this case I assume rsync is not smart enough nor does it try to correct the contents of symlinks for the relative directory changes.  Is this correct?  This is okay, it doesn't matter if the links are broken in the backup directories so long as they would be fixed and working if such time comes when they need to be restored. Today while troubleshooting a service broker problem, I discovered that the database owner was the Windows login of an employee who had left the company. His login had been removed and thus the query notifications were failing.   Supposedly the best practice for dealing with this is to make 'sa' the database owner. We changed it and that cleared out the queue.   My (very elementary) question: what is the database owner and what is its purpose? Suppose that $a_1,a_2, \cdots, a_n$ are $n$ different integers. Then $[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$.   I've no idea why it is true. Thanks very much. Underlined math in a Beamer presentation: felt-tip marker underlining I have an existing trigger which converts leads into peron accounts if the company name is blank.  Trigger AutoConvert on Lead (after insert) {      LeadStatus convertStatus = [           select MasterLabel           from LeadStatus           where IsConverted = true           limit 1      ];      List&lt;Database.LeadConvert&gt; leadConverts = new List&lt;Database.LeadConvert&gt;();       for (Lead lead: Trigger.new) {           if (!lead.isConverted &amp;&amp; lead.Company == null) {                Database.LeadConvert lc = new Database.LeadConvert();                String oppName = lead.Name;                 lc.setLeadId(lead.Id);                lc.setDoNotCreateOpportunity(true);                lc.setConvertedStatus(convertStatus.MasterLabel);                 leadConverts.add(lc);           }      }       if (!leadConverts.isEmpty()) {           List&lt;Database.LeadConvertResult&gt; lcr = Database.convertLead(leadConverts);      } }   I need to also write a trigger that stops records from coming into Salesforce if that email already exisits in a contact or an account (we use person accounts).  The issue is how do I get it working with the existing trigger (I need it to run before the trigger that converts it into a person account is run).   Is there a way to combine the two or add the functionality to create the record only if the email address doesn't already exist as a contact in the org? Getting / setting file owner in C# How is Cycles different from Blender Internal? How does Cycles work and how is it different from Blender Internal?  Which is better? Argue by contradiction to show that there is no surjection... from $A$ to $\{0,1\}^A$. When $A$ is any (possibly infinite) set  How does one go about this? execute command on a defined range of directories Is it possible to 'partition' a directory listing - say in to blocks of some number, to perform different actions on each 'range'?  For example, lets say I have the following directories inside another folder:  $ ls test abc/ def/ hij/ klm/ nop/ qrs/ tuv/ wxy/ zzz/   And I want to perform some action on the first 3 directories, another on the second 3, and so on.  My thought was that perhaps a loop across numbers would work, based on the output of something like ls | nl (but before anyone mentions it, I know parsing ls is a no-no!)  This obviously doesn't work, but illustrates my point I hope:  for dir in `ls | nl`;  do     do-something-with ${dir{1..3}} # Where $dir has taken on some numerical value linked to the folder)     do-something-with ${dir{4..6}}  # And so on...     do-something-with ${dir{n-3..n}}  done   The folders I intend to actually do this on, can be worked on in any order (i.e. the final splits can be totally arbitrary), but they have no logical naming consistency - by which I mean they can't be organised sensibly alphabetically or numerically based on any key within the directory name themselves. The  prohibited the development or use of cloaking technology by the Federation. This treaty was a peace treaty and use of cloaking technology in one's own space couldn't disturb peace. Plus, the Romulans already had cloaking technology, so banning it was unfair for the Federation. So, why was this ban introduced?  Another thing: There were many things to ban, but why cloaking technology? How do I summon mobs with block heads on Minecraft? My months and days in my File Manager are in German, how do I change that? On the photo you see 'Dez' : It means Dezember (German for December). I also saw one day Mittwoch (German for Wednesday). How do I change that German issue? This is only my File Manager and not completly but partially. Weird. The PHB states: "A familiar can’t attack, but it can take other actions as normal."  What can a familiar do? Can it use a potion of healing on a character? Can it drop caltrops? Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.   I have already figured out that $|Z(G)| = p$, and that $G'=[G,G] \lhd G$.  Also, $|G'| = p$ or $p²$.  I suppose I'd have to prove that $G' \subset Z(G)$, but I've been trying and I have no idea how. Any hints? Thanks! Sometimes I use, $PROJECT_HOME/* to delete all files in the project. When the environment variable, PROJECT_HOME is not set (because I did su and the new user doesn't have this environment variable set), it starts deleting all files from the root folder. This is apocalyptic.  How can I configure bash to throw error, when I use an undefined environment variable in the shell? No, actually I didn't, but that was a close call and I'm really curious how would one go about that one.  On my third or fourth visit to the Nether, I still didn't realize the risk, and didn't place marks that would help me get back to the origin (currently I like to use flint and iron to create big flaming arrows towards the exit, visible from afar.) I wandered past one hill, and then I couldn't locate the place I came from. I wisened up and started placing marks in form of torches, towers of netherrack with glowstones on top etc. The bunch of wood I had in my stash has proven invaluable as I ran out of steaks, and had to craft a bowl and start making mushroom soup. I realized the fastest way back would be to simply die, but since I had no clue where I was, that would mean losing my quite precious equipment, which cost me a lot of time and effort to gather and enchant, for that trip specifically. I also knew I had traveled rather far from the portal before starting placing marks, so the chances of finding it again by going in any random direction were rather slim.  By sheer luck I found one of the caverns I had explored before, and found my way back, but that was really a close call and I'd prefer to know any hints what to do in Nether if you're already lost (no Obsidian to build a new portal, not willing to die and forgot the direction to the exit.) $M$ = mass of the Sun  $m$ = mass of the Earth  $r$ = distance between the Earth and the Sun  The sun is converting mass into energy by nuclear fusion.   $$F = \frac{GMm}{r^2} = \frac{mv^2}{r} \rightarrow r = \frac{GM}{v^2}$$  $$\Delta E = \Delta M c^2 = (M_{t} - M_{t+\Delta t}) c^2 \rightarrow \Delta M = \Delta E / c^2$$  $$\rightarrow \frac{\Delta r}{\Delta t} = \frac{G}{v^2 c^2}.\frac{\Delta E}{\Delta t}$$  Sun radiates $3.9 × 10^{26}~\mathrm W = \Delta E/\Delta t$  Velocity of the earth $v = 29.8 \mathrm{km/s}$  There is nothing that is stopping the earth from moving with the same velocity so for centripetal force to balance gravitational force $r$ must change.   Is $r$ increasing? ($\Delta r/ \Delta t = 3.26070717 × 10^{-10} \mathrm{m/s} $)