Trying to find the principal value of the above equation I've done the first couple lines \begin{align} &amp;e^{(1+i)(\log(-1+\sqrt{3}i)}\\ &amp;e^{(1+i)(\ln(2)+\frac{2\pi}{3})} \end{align} How would I further simplify this?
How do I compute the principal value of a these complex numbers? I have 2 examples I'm not sure how to calculate One being $$\frac{1}{(1+i)^i}$$ the other is $$(-1+i\sqrt{3})^{1+i}$$ Can anyone help please? Anything appreciated
Windows losing IPv6 address after ~10 minutes When I initially connect to my home network my windows PC is assigned an IPv6 address - however after a few minutes it loses this address! I seem to have similar behaviour on multiple hosts using both wireless and wired connections.  My router is an Asus RT-AC87U.  How could it be losing the IPv6 address? How can I mintor / diagnose this issue?  Update:  Based on @grawity's suggestion below I ran wireshark on this. Sure enough I see a Router Solicitation message and a Router Advertisment message with a Router lifetime of 600 seconds. After 600 seconds my computer drops its Ipv6 address.  What is supposed to happen? Should my host send another Router Solicitation message? Or should the router periodically resend the Router Advertisment message?  Update 2:    says that Router Adverticement messages should be sent periodically. How to say the /p/ sound in the middle of words? 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Is there something I'm doing wrong or is it Blender? A question about $f(x)\equiv 0$ Dodecagon Area Question The distance between two opposite vertices of the dodecagon is 2. Find the area of the dodecagon.  Is there any way to do this without trigonometry?  And could you include a proof also? :O Why are some applications so hard to find in the Ubuntu Software Centre? Some applications don't pop up in the search even when you type in their name. Take for instance Sushi. When you type in "sushi" into the search box, it fails to throw up the application. Only when you type in "gnome-sushi" does it appear. This is despite the fact that the application has "sushi" by itself in the application description. There are other applications which don't spring to mind right now, but I've discovered before. Draw a vector with mathematica Casting a function pointer to another type Let's say I have a function that accepts a void (*)(void*) function pointer for use as a callback:  void do_stuff(void (*callback_fp)(void*), void* callback_arg);   Now, if I have a function like this:  void my_callback_function(struct my_struct* arg);   Can I do this safely?  do_stuff((void (*)(void*)) &amp;my_callback_function, NULL);   I've looked at  and I've looked at some C standards which say you can cast to 'compatible function pointers', but I cannot find a definition of what 'compatible function pointer' means. How to fix "Package is in a very bad inconsistent state" error? I can't update my system because it freezes while installing a third-party update (zramswap-enabler)! Sometimes I get the following message in Update manager:  Could not initialize the package information An unresolvable problem occurred while initializing the package information. Please report this bug against the 'update-manager' package and include the following error message: E:The package zramswap-enabler needs to be reinstalled, but I can't find an archive for it.  I tried to remove the zramswap-enabler, but it's impossible because I get the following message: dpkg: error processing zramswap-enabler (--remove):  Package is in a very bad inconsistent state - you should  reinstall it before attempting a removal. Errors were encountered while processing:  zramswap-enabler E: Sub-process /usr/bin/dpkg returned an error code (1)  Actually I would really reinstall that package, but it is unable to do it! If I remove this third-party PPA then the system is warning me about a very very serious problem. So why can I not install/reinstall/remove/update this package and why freezes the updater if I try to update? print python stack trace without exception being raised Copying unicode symbols from Firefox address bar as is Let's say I open a webpage with some Unicode characters, say, Cyrillic, in the address like this:        When I try to copy it from the address bar somewhere else, it becomes unreadable rubbish:        I guess this is for compatibility. However for readability I want to copy it straight away with proper Unicode characters.  What and how should I tweak to make that possible?  Edit: The answers are good, but they are hacky. Are there any settings in about:config? Would the One Ring have stayed hidden if Bilbo hadn't turned up? As much as I have tried, it doesn't seem possible to use separate labels when using a casesconstruction (from the amsmath package).  Ideally, I would like to be able to write something like  \documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation} f(x)=\begin{cases}   1&amp;x\geq0\label{positive}\\   0&amp;x&lt;0\label{negative} \end{cases} \end{equation} \end{document}   and later refer to both cases at different places. What would be the best way to achieve this result? Default gender, "Male" or "Female" Should our default gender when selecting male/female on the dropdown list be based on the local  (if a country have more female than male then female is the default value)? GParted can't resize partition, but unallocated partition is available I just came across this idiom in some open-source Python, and I choked on my drink.  Rather than:  if isUp:     return "Up" else:     return "Down"   or even:  return "Up" if isUp else "Down"   the code read:  return isUp and "Up" or "Down"   I can see this is the same result, but is this a typical idiom in Python? If so, is it some performance hack that runs fast? Or is it just a once-off that needs a code review? To perform a bit flipping attack, the previous block is modified by using XOR. This results in an altered plaintext. However, now the ciphertext of the previous block is altered, hence it will result in an invalid format. Am I correct or am I missing something?   For example, suppose I have the following plaintext name=jcconvenant;photo=picture.jpg;admin=false;colour=red;  and the correspoding ciphertext c26a5697689463d662f540e55e2a1ecef9c5df20133dfe49d6d3c369679a95ff4f4c5a490f530b2a2f25db40da64f1e9302724ce61b9a435e23f4d600252a143  Suppose we perform a bit flipping attack and get the following ciphertext c26a5697689463d662f540e55e2a1ecef9c5df20133dfe49d6c1d07071c495ff4f4c5a490f530b2a2f25db40da64f1e9302724ce61b9a435e23f4d600252a143  Then the resulting plaintext will still look corrupted.   ¶ä╚°  h8ì│►Nƒz│Ioé¤ßkü2KÀQiý4I@pg;admin=true;;colour=red;  Is there a way to perform bit flipping while still obtaining a valid plaintext? Selecting attributes or rows of polygons that intersect two attributes of overlaying polygon using ArcGIS Pro How do I convert a Word file's references to .bib format How do I convert a Word file's references to .bib format? Is any tool available  to convert it to .bib format?