query: Rigorous proof of the argument that one cannot square $-1$ in complex number problems
positive_passages.docid: 11089
positive_passages.text: For which complex $a,\,b,\,c$ does $(a^b)^c=a^{bc}$ hold?
negative_passages.docid: 14447
negative_passages.text: Direct proof that $\pi$ is not constructible
negative_passages.docid: 59639
negative_passages.text: Intuitive explanation of Residue theorem in Complex Analysis
negative_passages.docid: 45460
negative_passages.text: Proof verification of a number theory problem involving sequences.
negative_passages.docid: 125324
negative_passages.text: Fundamental Theorem of Algebra - an elementary complex analysis proof?
negative_passages.docid: 73687
negative_passages.text: Powers of $i$ in Complex Numbers.
negative_passages.docid: 104548
negative_passages.text: Geometric proof for irrationality of $\pi$
negative_passages.docid: 63255
negative_passages.text: Proving an entire, complex function with below bounded modulus is constant.
negative_passages.docid: 11506
negative_passages.text: Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
negative_passages.docid: 95105
negative_passages.text: Solutions in complex number field, instead of $\mathbb{N}$, to Fermat's Last Theorem
negative_passages.docid: 23752
negative_passages.text: Proving Irrationality
negative_passages.docid: 93606
negative_passages.text: Showing that $C[0,1]$ is not complete
negative_passages.docid: 106716
negative_passages.text: The sum of square roots of non-perfect squares is never integer
negative_passages.docid: 107450
negative_passages.text: False proof that $ρe^{iθ} = ρ$ and so complex numbers do not exist?
negative_passages.docid: 68233
negative_passages.text: Fermat's little theorem's proof for a negative integer
negative_passages.docid: 139168
negative_passages.text: Prove that there is an unique $z$ s.t. $f(z) = z$ where $z$ is a complex number
negative_passages.docid: 95057
negative_passages.text: Possible fake proof of $1= -1$