Determine the fourth roots of -16 in the form $x +iy$ where $x$ and $y$ are not trigonometric functions.  I do not even know what they really want from me in this question.  My initial thought wass: $\sqrt[4]{-16} = 0 + 2i = 2i$  but that seems overly simplistic for a problem that counts as 8 points in an exam.
Probably dumb question, but I would like to ask it anyway.  I was to solve this equation:  $z^4 = -16$  At first glance, the way to solve it would be (as any other equation):  $z^2 = \sqrt{-1} * 4 \lor z^2 = -\sqrt{-1} * 4$  $z^2 = 4i \lor z^2 = -4i$  $z = 2\sqrt{i} \lor z = -2\sqrt{i} \lor z = 2i\sqrt{i} \lor z = -2i\sqrt{i}$  However, in suggested answers, there are $z_1, z_2, z_3$ and $z_4$ found using trigonometric formulas. Is there something particulary wrong in my solution and the only proper one uses trigonometric form of complex number?
yum install error I can't run a yum command on my server without getting this:   CRITICAL:yum.cli:Config Error: Error accessing file for config file:///etc/yum.conf   This is what my yum.conf looks like:  # This is the fedorafaq.org yum.conf for Fedora Core 5. # # Note that you also need the rest of the configuration # as described at http://www.fedorafaq.org/#yumconf  [main] cachedir=/var/cache/yum keepcache=0 debuglevel=2 logfile=/var/log/yum.log exactarch=1 obsoletes=1 gpgcheck=1 plugins=1 metadata_expire=1800  # PUT YOUR REPOS HERE OR IN separate files named file.repo # in /etc/yum.repos.d   This is what my yum.repos.d looks like:  fedora.repo fedora-updates.repo fedora-updates-testing.repo   The permissions on those files are 0666 and it won't allow me to make them root:root Car parking related probability PGFplots foreach equivalent to TikZ's with multiple variables separated by a slash Will i be granted ESTA after getting rejected thrice on different nationality? I had applied for B1/B2 on my previous nationality but it got rejected Thrice.  I had planned on visiting my mother as she lives there. my last refusal was 3 years back. Now i have gained an European nationality and I am thinking of applying for ESTA so I can visit my mother. I have doubts if it will be accepted because I'll have to disclose about my previous refusals.  What should I do? because if I don't disclose my previous refusals I fear I might be rejected permanently. Is the cube root of a prime number rational? The question is: if $P$ is prime, is $P^{1/3}$ rational?   I have been able to prove that if $P$ is prime then the square root of $P$ isn't rational (by contradiction) how would I go about the cube root? Einstein's big revelation was that time and space are inseparable components of the same fabric. Physical observation tells us that distant galaxies are moving away from us at an accelerated rate, and because of the difficulty (impossibility?) of defining a coordinate system where things have well defined coordinates while also moving away from each other without changing the metric on the space, we interpret this to mean that space itself is expanding.   Because space and time are so directly intertwined is it possible that time too is expanding? Or perhaps it could be contracting? How to loop through a HashMap in JSP? Do I need a transit visa in Zurich on the way to India? I am travelling from US to India, with an Indian passport but expired F1 visa and going there to get my H1B visa stamping. I have a stop at Zurich for 2 hours while flying to India. Do I need a transit visa for my trip? Is spacetime discrete or continuous? Finding functions such that $f(g(x)) = f(x)g(x)$ Let's assume the functions in question are continuously differentiable. If $f(g(x)) = f(x)g(x)$, then: $$f'(g(x))g'(x) = f'(x)g(x)+f(x)g'(x)$$ I attempted to find a particular solution by letting $g(x) = x$. Then, $$f'(x) = xf'(x) + f(x)$$ $$df = xdf + fdx$$ $$\frac{df}{f} = \frac{dx}{1-x}$$ $$\ln(f(x)) = -\ln(1-x)+C$$ $$f(x) = \frac {A}{1-x}$$ Where $A$ is a constant. This solution was fairly unsatisfying to me, and upon checking it, I see it doesn't actually work, as letting $g(x) = x$ leads to $f(x) = xf(x)$. I was wondering if there were better answers, or at least a less trivial way to go about the problem. Why do return flight costs vary depending on the country of origin? Make gnome-terminal show the command running as title I want the name of command running , e.g unzip to be visible through the title bar of gnome-terminal , but it seems to be impossible , if the application running doesn't set a title explicitly , even though I choose 'Replace initial title' option in the profile dialog. My settlement was attacked by some Raiders and my defenses took care of them along with some of my NPC's. It seems like the Raiders didn't make it through to any of the buildings. What happens when they do?  Can you lose your items if you stored them in a house?  Can the NPC's die?  Do the enemies destroy your buildings? When I apply to a PhD program, may I ask a postdoc who closely supervised me to write a recommendation letter? My supervisor also has written one for me, but I believe the postdoc can comment on my research skills in a more detailed and precise way. Does a postdoc have enough authority to convince admission committee? I was wondering in C++ if I have an enum can I access the value at the second index?  For example I have  enum Test{hi, bye};   if I want 'hi', can I do something like Test[0], thanks. Is there a gender-neutral pronoun that can replace “his” or “her”? How can I stop being prompted to unlock the 'default' keyring on boot? Whenever Ubuntu boots up, a dialogue pops up asking me to unlock my default keyring. Is there some way this can unlock automatically through PAM or some other magical way? "Requires 50 reputation" to comment on deleted posts So I recently saw add comment (requires 50 reputation) on a deleted answer. After looking around a bit, it seems to be on all deleted posts now (only deleted posts, normal posts still say just add comment).  I'm sure it wasn't there before (I think it just said add comment (unclickable) or possible nothing).  It is also on , presumably the root cause is the same.  And yes, I do have more than 50 reputation (in case anyone was wondering).  Just to clarify, requires 50 reputation obviously shouldn't be there for users with 50 or more reputation. Choices:   Display nothing Unclickable add comment - probably not ideal Unclickable add comment (disabled for deleted posts) or something along those lines   FYI - You may be somewhat confused right about now if you can't  yet. I cleared all my browser data and visited  and it logged me back in. How?  This happens on Chrome on OS X and Windows 7.  Surely the security concerns outweigh the benefits to the user. What if a family member or friend wants to use my machine? I wouldn't want them logged in as me.  Update  My mistake, I should have said data &#8212; all those checkboxes clicked/checked. I completely cleared everything, yet it still logs me back in.  Update 2  Here's a video to prove it: Does casting blindness on a Medusa (or other gaze using creature) stop their gaze attack?