query: Why is $sinx$ the imaginary part of $e^{ix}$?
positive_passages.docid: 742
positive_passages.text: How to prove Euler's formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$?
negative_passages.docid: 140851
negative_passages.text: Precalculus unit circle with imaginary axis.
negative_passages.docid: 95108
negative_passages.text: Alternative form of ArcSin[Sin[x]]
negative_passages.docid: 81571
negative_passages.text: Complex Exponent of Complex Numbers
negative_passages.docid: 132525
negative_passages.text: Real Numbers Raised to Imaginary Powers?
negative_passages.docid: 100968
negative_passages.text: Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
negative_passages.docid: 91521
negative_passages.text: Ambiguity of notation: $\sin(x)^2$
negative_passages.docid: 140459
negative_passages.text: Why is $\left(e^{2\pi i}\right)^i \neq e^{-2 \pi}$?
negative_passages.docid: 58947
negative_passages.text: Integral of $\int\sin^{3}xdx$
negative_passages.docid: 120092
negative_passages.text: Express the complex numbers given in Problem in the form $a+ib$
negative_passages.docid: 40837
negative_passages.text: Why $e^{i(π/3)} \ne -1$?
negative_passages.docid: 17620
negative_passages.text: Why the principal value of complex number argument is taken within $(-\pi,\pi]?$
negative_passages.docid: 127799
negative_passages.text: Eigenvalues of symmetric matrices are real without (!) complex numbers
negative_passages.docid: 84826
negative_passages.text: Evaluating $\int_0^{2 \pi} e^{\cos x} \cos (nx - \sin x) \,dx$ using complex analysis
negative_passages.docid: 4693
negative_passages.text: what is the$ \int \sin (x^2) \, dx$?
negative_passages.docid: 103487
negative_passages.text: Integration of the cardinal sine
negative_passages.docid: 140381
negative_passages.text: Mclaurins with $e^{\sin(x)}$