query: Find the locus of $|z-2i|=3|z+3|$
positive_passages.docid: 143100
positive_passages.text: Identify the plane defined by $|z-2i| = 2|z+3|$
negative_passages.docid: 116223
negative_passages.text: Show that the angles satisfy $x+y=z$
negative_passages.docid: 87029
negative_passages.text: Solve $y^2=x^3-4$ in $x,y\in \mathbb{Z}$
negative_passages.docid: 56341
negative_passages.text: Solving complex numbers equation $z^3 = \overline{z} $
negative_passages.docid: 108775
negative_passages.text: Identify the ring $\mathbb {Z}[i]/(2 + i) $
negative_passages.docid: 77903
negative_passages.text: Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
negative_passages.docid: 101320
negative_passages.text: How to tell $i$ from $-i$?
negative_passages.docid: 10589
negative_passages.text: How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?
negative_passages.docid: 17508
negative_passages.text: Knowing $|z|$ and $|w|$ (and possibly $z\overline{w}$), what are $|z+w|^2$, $|zw|^2$, $|z-w|^2$, $|z/w|^2$?
negative_passages.docid: 79808
negative_passages.text: Prove the representation of complex numbers is parallelogram
negative_passages.docid: 118299
negative_passages.text: Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
negative_passages.docid: 71074
negative_passages.text: The locus of the intersection point of two perpendicular tangents to a given ellipse
negative_passages.docid: 141391
negative_passages.text: how to find $\Gamma(n+3/2)$
negative_passages.docid: 63742
negative_passages.text: A key doubt about the resultant of two polynomials and their common zero locus
negative_passages.docid: 68915
negative_passages.text: What are the units in $\mathbb{Z}[\root 3 \of 2]$?
negative_passages.docid: 61466
negative_passages.text: what is $\int_{|z|=3}\frac{1}{(z-2)^n(z-4)^m}dz$ for $m,n\in\mathbb{N}$?
negative_passages.docid: 22084
negative_passages.text: $\mathbb{Z}[i] / (2+3i)$ has 13 elements