query: What does $2|z+3i|=|z-i|$ represent?
positive_passages.docid: 122060
positive_passages.text: Apollonius circle, its radius and center
negative_passages.docid: 30172
negative_passages.text: Why is the order of $\mathbb{Z}[i]/\langle 3+i\rangle$ equal to 10?
negative_passages.docid: 141961
negative_passages.text: What is the difference between [[ $a == z* ]] and [ $a == z* ]?
negative_passages.docid: 87322
negative_passages.text: How to calculate $i^i$
negative_passages.docid: 79808
negative_passages.text: Prove the representation of complex numbers is parallelogram
negative_passages.docid: 126859
negative_passages.text: $\Bbb Z^\ast$ What is this notation?
negative_passages.docid: 24688
negative_passages.text: Why are $i$ and $-i$ "more indistinguishable" than $\sqrt{2}$ and $-\sqrt{2}$?
negative_passages.docid: 124116
negative_passages.text: What does the notation $\binom{n}{i}$ mean?
negative_passages.docid: 27062
negative_passages.text: Given complex $|z_{1}| = 2\;\;,|z_{2}| = 3\;\;, |z_{3}| = 4\;\;$ : when and what is $\max$ of $|z_{1}-z_{2}|^2+|z_{2}-z_{3}|^2+|z_{3}-z_{1}|^2$
negative_passages.docid: 120235
negative_passages.text: Clarification of the notation $f: \mathbb{R} \setminus\{3\} \to\mathbb{R}\setminus\{2\}$
negative_passages.docid: 95449
negative_passages.text: What is the square root of "$i$"?
negative_passages.docid: 86197
negative_passages.text: Let $z_1 = x_1 +iy_1 $ and $z_2 = x_2 +iy_2$ be two complex numbers. The dot product of $z_1$ and $z_2$ is defined by $ = x_1x_2+y_1y_2$
negative_passages.docid: 90549
negative_passages.text: If $z^2 = z_1^2+z_2^2+z_3^2$ then $|\Re(z)| \le|\Re(z_1)|+|\Re(z_2)|+|\Re(z_3)|$
negative_passages.docid: 133852
negative_passages.text: What is the value of $i^{i^{i^\ldots}}$?
negative_passages.docid: 105727
negative_passages.text: Why is the complex number $z=a+bi$ equivalent to the matrix form $\left(\begin{smallmatrix}a &-b\\b&a\end{smallmatrix}\right)$
negative_passages.docid: 156782
negative_passages.text: Confused about complex numbers
negative_passages.docid: 57659
negative_passages.text: Evaluate $\int_{\left | z \right |=3} (e^{z}-1)dz/(z(z-1)(z-i))$