I have to show that $(z^*)^5=1$, if $z^5=1$, but how do I do that? I tried to show it by inserting $x-yi$ into the equation, so $(x-yi)^5=1$. After using the binomial formula for a power of $5$, I thought I might be able to see similarities between the imaginary and real parts but I just got a complete mess. I'd be happy if someone could help me.
If an polynomial has a complex root, is it necessary that the conjugate of that root is also a root of the polynomial? I am not sure about this. Please comment on this.
fontenc vs inputenc I've got a couple of URL autocomplete suggestions where Chrome suggests the wrong URL consistently.   How can I delete the incorrect entry from the address bar's suggestion list? The page I want shows up too but it's never the first result. What's the grammar behind "A'warring", from the lyrics of Symphony of Destruction? What's the grammar behind A'warring, from the lyrics of Symphony of Destruction by Megadeth? It's the first time I'm seeing the use of such apostrophe. A two way String hash function Why does the question's closed status disappear when clicking to load a new edit? I've been through the Windows 10 upgrade, and am experiencing a recurring "INTERNAL_POWER_ERROR", which is stopping me from logging in.  I'd like to be able to try to boot to safe mode, but it appears that pressing F8 during boot is no longer enough, so how can I boot in safe mode (or any of the other recovery options) on a Windows 10 PC that doesn't let me log on? Touch enabled monitors and Android Getting incorrect slope values from an ASTER DEM in QGIS? Dropping the '-ing' in noun adjuncts I always remember many verbs ending in -ing.  Swimming club/cap and shaving foam for example. I now see increased use of swim club and shave foam.  Why has this happened, is it correct use of English ? XSL That Returns the XML unchanged I am looking for a XSL snippet that simply returns the XML unaltered. It sounds trivial but I can't seem to find an example anywhere on the web. Any help out there? In C++, what is a virtual base class? I want to know what a "virtual base class" is and what it means.  Let me show an example:  class Foo { public:     void DoSomething() { /* ... */ } };  class Bar : public virtual Foo { public:     void DoSpecific() { /* ... */ } }; What's the maximum value for an int in PHP? Ignoring the special libraries that allow you to work with very big numbers, what's the largest int value you can store in PHP? I have a brand new 32GB flash drive that was bought from Hong Kong but manufactured in China.  When I plug it in, it's detected, and when I examine the properties of the drive the size is reported to be 31.2 GB.  Windows forces me to format it but I have not manged to actually do that.  I then I browsed the internet and a forum told me to change the letter to L. After I did that I searched many programs that can help me format it, but when I checked it back, it is 4MB now.  Any idea what's happening with my drive? Removing unwanted appearance of underlying mesh Indent entire section using only preamble I heavily use org-mode in Emacs to create TODO lists with timekeeping, which has a handy export to LaTeX feature. The problem is that in order to get my exported LaTeX document to look right, I want to indent entire sections, essentially treating sections like lists. It's very easy to create a template to copy and paste into every new file, but not feasible to edit the text directly as this would interfere with org-modes ease of use. Thus:  Is there a way to indent an entire section, using only the preamble?  MWE  \documentclass{article} \usepackage[explicit]{titlesec} \setcounter{secnumdepth}{0} \newcommand{\clock}{CLOCK: number number number \\}  \titleformat{\section}{\bfseries{}}{\roman{section}}{3pt}{#1} \titlespacing*{\section}{0pt}{0pt}{0pt} \titleformat{\subsection}{\bfseries{}}{\roman{subsection}}{3pt}{$\rightarrow$#1} \titlespacing*{\subsection}{2em}{0pt}{0pt} \begin{document}   \section{First section} \clock  \section{Second section} \clock \clock \clock  \subsection{First subsection} \clock \clock  \subsection{Second subsection} \clock  \subsection{Third subsection} \clock  \end{document}   I want the text with the red arrow to be indented to the same level as the section. Should Community Moderators be "elected for life", or have terms? While I applaud the excellent work of , the question has come up:     How long will be the elected moderator’s “mandate”? Is it for life, or are we going to have “moderator elections” regularly?   Of course, any community moderator who wishes to recuse him or herself can certainly do that at any time.   Should we have term limits that require community moderators be cycled out periodically, so others get a chance to moderate? Should we hold regular (say, yearly) moderator elections? Is it better to have a larger pool of community moderators, and let the normal ebb and flow of turnover get us "natural" variability in moderation?   What are your thoughts on this? Let $f(z)$ be a holomorphic function on a disk of radius $&gt;1$ about the origin, and suppose that $|f(z)|\leq 1$ for $z$ with $|z|=1$ and $\text{Re}(z)&gt;0$ and $|f(z)|\leq 2$ for $z$ with $|z|=1$ and $\text{Re}(z)\leq 0$.  How does one show the bound $|f(0)|\leq \sqrt{2}$? No continuous function switches $\mathbb{Q}$ and the irrationals Can you have a class in a struct? How should a user's death be handled? It is a bit of a morbid concept, but having recently had a friend die unexpectedly and having to deal with the online repercussions of this event has gotten me to thinking about what should happen to my accounts when I kick the bucket.  I haven't had any great insights yet, but here are some things I think are worth thinking about:   an entry in the FAQ telling the person's loved ones what to do with respect to the account would be extremely helpful, specifically who to contact, how to contact them, and what proof is necessary some form of optional date of death on the user account screen some way to mark the user as no longer being able to generate content and blocking any attempt to login as the user.   The danger I see in implementing such features is the possibility of someone faking another person's death and thereby locking a user out of his or her account or worrying his or her friends.