query: Does imaginary numbers correspond to a real phenomenon?
positive_passages.docid: 153976
positive_passages.text: Do complex quantities and irrational numbers exist in nature?
negative_passages.docid: 51191
negative_passages.text: Does a negative number really exist?
negative_passages.docid: 13794
negative_passages.text: $|z_{1} + z_{2}| = |z_{1} - z_{2}| \implies z_{1}/z_{2}$ is Imaginary
negative_passages.docid: 92595
negative_passages.text: A problem regarding the in-equality of complex numbers .
negative_passages.docid: 36192
negative_passages.text: Are virtual particles only a fictive tool in equations?
negative_passages.docid: 7672
negative_passages.text: Are there strange attractors whose coordinates are "almost integers"?
negative_passages.docid: 127537
negative_passages.text: Is there any mathematical or physical situations that $1+2+3+\ldots\infty=-\frac{1}{12}$ shows itself?
negative_passages.docid: 21606
negative_passages.text: Can all real numbers be represented by the sum of a convergent series?
negative_passages.docid: 30817
negative_passages.text: Is an automorphism of the field of real numbers the identity map?
negative_passages.docid: 140851
negative_passages.text: Precalculus unit circle with imaginary axis.
negative_passages.docid: 29064
negative_passages.text: Can the real and imaginary parts of $\dfrac{\sin z}z$ be simplified?
negative_passages.docid: 56745
negative_passages.text: Why does this not work with an imaginary exponent?
negative_passages.docid: 10357
negative_passages.text: Do harmonic numbers have a “closed-form” expression?
negative_passages.docid: 47845
negative_passages.text: Mirror algorithm for computing $\pi$ and $e$ - does it hint on some connection between them?
negative_passages.docid: 2796
negative_passages.text: How to tell Mathematica that certain variables are real/imaginary, integer-valued, etc
negative_passages.docid: 154411
negative_passages.text: How can I intuitively understand complex exponents?
negative_passages.docid: 62297
negative_passages.text: What can be said about complex numbers $z_1, z_2, z_3$ if $\frac{z_1 - z_3}{z_2 - z_3}$ is real?