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 May13 awarded Caucus Apr27 comment How do you solve $z^4 = 2(1+i\sqrt{3})$ @RaymondManzoni He knows that the exponential form for a complex number is composed of two parts the "modulus" and the "argument". He doesn't seem to know how those are defined (hence why I suggested he reread the definitions carefully). How would he understand that equivalence without that knowledge? And you are right about him not claiming that he didn't know it. But uh I haven't claimed to not know the proof for Fermat's Last Theorem. Valid to suggest that I do know it? Whatever, separate argument. Apr27 comment How do you solve $z^4 = 2(1+i\sqrt{3})$ Where did he claim to understand the equivalence: $z^4 = 4e^{i\pi/3}$ ? I really think he needs to take this slower and that the existing answers aren't of much help to him. But perhaps it's the wrong forum too. Apr27 comment How do you solve $z^4 = 2(1+i\sqrt{3})$ Try the easier problem where we want to transform $z = 2(1 + i\sqrt{3})$ into its trigonometric form instead of $z^4 = 2(1 + i\sqrt{3})$. If you can do that then you can do one of the main steps for your original problem. You should be able to do the easier problem by just rereading the definitions carefully and drawing it on paper. Apr27 comment How do you solve $z^4 = 2(1+i\sqrt{3})$ @maxmitch Do you understand the goal of this question? Meaning, do you understand the two ways to represent $z$? One is the "cartesian" coordinates for $z$ and the other is "trigonometric". Euler's identity helps you perform this transformation because taking the 4th root of $z$ is ugly when you don't have it in the "complex exponential" form (the $e^{i\alpha}$ stuff). Apr27 comment Addition table for a 4 elements field If you literally relabel: $0 \rightarrow a$ and $a \rightarrow 0$ then why would this addition table be less valid (other than the fact that it is a bit unintuitive because the identity element is labeled $a$ instead of $0$)? Jan28 comment How to formally write a property of a specific coloring of a graph. I think you meant $Z(u) = Z(v) \leftrightarrow i = k$ Nov23 comment Why is “the set of all sets” a paradox? @JustinL. Sure... but it requires Cantor's theorem to prove. You can prove that it must contain a "paradoxical set" with a diagonalization argument directly (of course that argument is essentially the one used to prove Cantor's theorem anyways). I should mention that the reason I have a natural disinclination for these proofs is because in my set theory course we were asked to prove a lot of theorems/lemmas without the assistance of stronger theorems. Nov21 comment Proving A Theorem Concerned With Prime Numbers They're just pointing out that $(i+2)$ is skipped in the product. For instance you can write $n! = 1 \cdot 2 \cdots n$, but if you want to remove say $k < n$ from that product you can do $1 \cdot 2 \cdots (k-1) \cdot (k+1) \cdots (n-1) \cdot n$. Nov21 awarded Commentator Nov17 comment Let $X = \Bbb{R}$ with the discrete metric. Is $X$ connected? Disclaimer: I remember nothing about metric spaces and topology. As a student, what really helped me with "formalizing proofs" was just using definitions as often as possible. So, for instance, your claim that "any nonempty subset $A \neq X$ is open", well you should prove it by using the definition of an open subset of the real number metric space. Your professor/teacher probably won't care, but it can help you if you think you are being "informal" (aka skipping steps that need to be proved). Nov12 comment There is solution for $x^{16} \equiv 256 \pmod p$ for all prime $p$. Prove or disprove it. @ShreevatsaR Ah my bad. I didn't read his comment at the bottom. Nov12 comment There is solution for $x^{16} \equiv 256 \pmod p$ for all prime $p$. Prove or disprove it. @yunone True... but Alex J Best's example isn't a counterexample in this case. Nov11 comment Vertical asymptotes, intervals of increase and decrease, local maxima and minima, concavity, inflection for $f(x)=1+(7/x)-(5/x^2)$ You've asked three questions on this one pset in the past 3 hours. You haven't demonstrated that you've put a significant amount of effort in any of the questions. What's even the point of doing this homework if you are just going to get SE to do it for you? Nov10 revised Tree problem about preorder notation added 241 characters in body Nov10 answered Tree problem about preorder notation Nov5 suggested rejected edit on (Basic) calculus proof. Nov4 answered Hamiltonian path in a tournament Nov4 comment Hamiltonian path in a tournament I don't have an answer yet but did you guys learn about the lower bound for comparison based sorts? The proof involves $log(n!)$ which is $\Theta(n \log n)$. Oct20 comment In how many ways can I have \$1.50 using exactly 50 Coins? I'm answering the question with a student's mindset. I would first see if I could solve it by hand. The next would be to solve it with an algorithm (well, programming it). I guess I have a hard time believing the OP literally just wanted to know that there were 10 ways to do this?