query: Are complex numbers really needed in quantum mechanics?
positive_passages.docid: 58122
positive_passages.text: QM without complex numbers
negative_passages.docid: 81571
negative_passages.text: Complex Exponent of Complex Numbers
negative_passages.docid: 153976
negative_passages.text: Do complex quantities and irrational numbers exist in nature?
negative_passages.docid: 23265
negative_passages.text: "Where" exactly are complex numbers used "in the real world"?
negative_passages.docid: 28514
negative_passages.text: Does FindFit support complex numbers or doesn't it?
negative_passages.docid: 107450
negative_passages.text: False proof that $ρe^{iθ} = ρ$ and so complex numbers do not exist?
negative_passages.docid: 124703
negative_passages.text: Where does the $i$ come from in the Schrödinger equation?
negative_passages.docid: 106940
negative_passages.text: Why are complex numbers considered to be numbers?
negative_passages.docid: 21917
negative_passages.text: Mathematical Prerequisites for QFT
negative_passages.docid: 105751
negative_passages.text: Why use coherent state path integral? What is its motivation or goal?
negative_passages.docid: 35307
negative_passages.text: Comparing complex numbers
negative_passages.docid: 47779
negative_passages.text: Why does this integral have a complex component?
negative_passages.docid: 148644
negative_passages.text: Definition of complex number
negative_passages.docid: 122166
negative_passages.text: Significance of $i$ in the Schrödinger equation
negative_passages.docid: 29064
negative_passages.text: Can the real and imaginary parts of $\dfrac{\sin z}z$ be simplified?
negative_passages.docid: 5032
negative_passages.text: Compute $e^{e^z}$, where z is a complex number
negative_passages.docid: 121728
negative_passages.text: Are "Complex Numbers" already defined in Objective-C?