query: real life application of imaginary numbers
positive_passages.docid: 23265
positive_passages.text: "Where" exactly are complex numbers used "in the real world"?
negative_passages.docid: 64671
negative_passages.text: What's the physical meaning of the imaginary component of impedance?
negative_passages.docid: 68976
negative_passages.text: Given real numbers: define integers?
negative_passages.docid: 43731
negative_passages.text: Real life uses of prime numbers (in physics/engineering)
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: 86381
negative_passages.text: What is imaginary time?
negative_passages.docid: 30462
negative_passages.text: What are the real-world applications of real analysis?
negative_passages.docid: 112348
negative_passages.text: Defining the Complex numbers
negative_passages.docid: 107704
negative_passages.text: Applications of complex numbers to solve non-complex problems
negative_passages.docid: 131505
negative_passages.text: Real world uses of Quaternions?
negative_passages.docid: 106197
negative_passages.text: Complex numbers - Exponential numbers - Proof
negative_passages.docid: 35307
negative_passages.text: Comparing complex numbers
negative_passages.docid: 128582
negative_passages.text: A reference request for real world experimental data
negative_passages.docid: 34709
negative_passages.text: Complex numbers - roots of unity
negative_passages.docid: 31900
negative_passages.text: Induction on Real Numbers
negative_passages.docid: 9737
negative_passages.text: Complex number operations: telling Mathematica variables are real