How to display array elements?
What's the simplest way to print a Java array?
Can ASP.NET MVC generate elements with lower case name and id attributes Get index of parent div from child divs Plot $|z - i| + |z + i| = 16$ on the complex plane Plot $|z - i| + |z + i| = 16$ on the complex plane   Conceptually I can see what is going on. I am going to be drawing the set of points who's combine distance between $i$ and $-i = 16$, which will form an ellipse. I was having trouble getting the equation of the ellipse algebraically.  I get to the point:  $x^2 + (y - 1) ^2 + 2\sqrt{x^2 + (y - 1)^2}\sqrt{x^2 + (y + 1)^2} + x^2 + (y+ 1)^2 = 256$  $2x^2 + 2y^2 + 2\sqrt{x^2 + (y - 1)^2}\sqrt{x^2 + (y + 1)^2} = 254$  It seems like I'm and doing something the hard way. 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. "Mornings came and cast a blinding sunlight over everything, and he felt like nothing worthwhile could be accomplished."  For some reason, I feel like "a blinding light" is ok, but if its sunlight, then I should drop the "a" and write "cast blinding sunlight", but I'm not sure why I feel this way.   Can anyone offer some enlightenment?  edit - alternate phrasing, closer to being a literal translation: "Mornings came without warning, flooding the day with a strong sun, and he felt like nothing worthwhile could be accomplished."   I would still like an answer to the technical question of whether I should drop the "a", but would also appreciate knowing if anyone thinks option #2 is a better choice. Renaming attributes/fields in shapefile attribute table using QGIS I would like to rename some fields in my attribute table:  Like rename &quot;XRF_N3&quot;in something else. It seems quite a easy issue but I don't find any information about how can I do that. List all columns for a specified table Is "TABLESAMPLE BERNOULLI(1)" not very random at all? Levels or First Differences, VECM or VAR for Ultimate Impulse Response Functions? How can you enumerate an enum in C#?  E.g. the following code does not compile:  public enum Suit {     Spades,     Hearts,     Clubs,     Diamonds }  public void EnumerateAllSuitsDemoMethod() {     foreach (Suit suit in Suit)     {         DoSomething(suit);     } }   And it gives the following compile-time error:     'Suit' is a 'type' but is used like a 'variable'   It fails on the Suit keyword, the second one. Solve the following system of equations  $ \begin{cases}  x_1^{'}(t)=x_1(t)+3x_2(t) \\  x_2^{'}(t)=3x_1(t)-2x_2(t)-x_3(t) \\  x_3^{'}=-x_2(t)+x_3(t)\end{cases} $.  First, I create the column vectors $X$ and $X^{'}$. Then the matrix $$A= \begin{bmatrix} 1 &amp; 3 &amp; 0  \\ 3 &amp; -2 &amp; -1 \\ 0 &amp; -1 &amp; 1  \\ \end{bmatrix} $$  Now, I find the eigenvalues, $-4,3,1$ and their corresponding eigenvectors $(-3,5,1)^T (-3,-2,1)^T (1,0,3)^T$.   I'm just not sure how to take it from here and solve the system of differential equations. I want a diagonal matrix $D$ so that I can read the solutions easy, but I'm not sure how to do it.  EDIT   Building on @Francisco 's answer, I'd have that:  $$X=c_1  (-3,5,1)^T  e^{-4t}   + c_2 (-3,-2,1)^T e^{3t} + c_3 (1,0,3)^T e^{t} $$.  But I believe this could be written in a simpler form. I'm trying to understand an algorithm that tries to map points from a lie group to its lie algebra using the exponential map. The background is the representation of 3d coordinate transformations as a lie group.  I can imagine, how one can map points on a manifold (eg a sphere) to the tangent space (tangent plane) at some point x on the sphere. I can imagine to create the tangent space by computing derivatives at that point x. But I cannot imagine how the exponential of some matrix is giving me that tangent space?  How can I envision the exponential of a matrix? Is there some picture or analogy I can use as intuition? Is the standard Canon 18-55 lens the same as 5 years ago? During my studying to integration I find this integration.  So I tried to prove but I got stuk.  So I need help in this integration.  $$\displaystyle\int_{-\infty}^{\infty} \frac{x \sin (x)}{1+x^2}  dx = \frac {\pi}{e} $$ By accident, I messed up a configuration file. How do I recover the default version without reinstalling or affecting other things? If every element of set A ia an element of set B then we say that A is subset of B. A is said to be proper subset if A does not equal B.  My question is - whether the symbol we use to show subset is  same as that for proper subset? I have seen that A is subset of A itself is shown by the same symbol as that for the subset while when we write improper subset, we usually write equal to sign with symbol of subset. So, please help me to know this. Variance of sample variance? What is the variance of the sample variance? In other words I am looking for $\mathrm{Var}(S^2)$.  I have started by expanding out $\mathrm{Var}(S^2)$ into $E(S^4) - [E(S^2)]^2$  I know that $[E(S^2)]^2$ is $\sigma$ to the power of 4. And that is as far as I got. How to show the full path of a file or directory in the terminal? I need to know how the directory name in order to type it out in the terminal. How do I access the names of directories?   Windows Explorer used to have a title bar with the full path. Can someone please help me figure out how to see the full path of a certain file? Windows 8.1 64-bit: High memory usage I have 8GB of memory on a 64 bit windows 8.1 machine, and windows is telling me I'm using 91% of my memory, yet its simultaneously telling me I'm only using 3GB.  I literally just restarted my machine a few minutes ago because it was being incredibly rediculously slow. I'm currently only running chrome (with a ton of tabs, but doesn't add up to anywhere near 7.5GB). What could be going on here?   Here's a bunch of my current info       I took a look at this:  but I wasn's able to use xperf and the rest didn't lead me to a solution.  UPDATE - RamMap:   UPDATE 2: I checked Resource Monitor at Wouter's suggestion and found an "Image" called lxdecoms.exe with over 6GB of Commt (KB). I tried killing the process, but while it lowered my Commit Charge, it didn't affect "Used Physical Memory". So I restarted hoping to capture it again in full, but its not back yet and yet the problem persists.  I should note that I do have a Centos virtual box virtual machine running on my machine, not sure if that has any weird memory impacts that aren't reflected in the numbers in these tools.   I got xperf working, so here's my resource monitor and a wpa analysis of my xperf output (from xperf -on ReferenceSet -BufferSize 1024 -MaxFile 512 -FileMode Circular  &amp;&amp; timeout 5 &amp;&amp; xperf -d MemUsage.etl):     What is N/A that's taking up 2.7GB of memory? My VM? I want to get that fancy LaTeX symbol to put in one of my documents but I cannot find it anywhere.  All searching for things like latex symbol have not resulted in the symbol but other symbols.