query: Where does complex number multiplication (as vectors, not referencing $i$) come from?
positive_passages.docid: 21769
positive_passages.text: Motivation for complex numbers
negative_passages.docid: 79808
negative_passages.text: Prove the representation of complex numbers is parallelogram
negative_passages.docid: 140829
negative_passages.text: What does $b_i\mid b_{i+1}$ mean in this context?
negative_passages.docid: 87322
negative_passages.text: How to calculate $i^i$
negative_passages.docid: 92647
negative_passages.text: How do I compute the principal values of these complex numbers
negative_passages.docid: 100968
negative_passages.text: Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
negative_passages.docid: 34709
negative_passages.text: Complex numbers - roots of unity
negative_passages.docid: 11809
negative_passages.text: Is there any isomorphism between the non-zero complex numbers under multiplication and the complex numbers under addition?
negative_passages.docid: 51314
negative_passages.text: How to prove that a complex number is not a root of unity?
negative_passages.docid: 120092
negative_passages.text: Express the complex numbers given in Problem in the form $a+ib$
negative_passages.docid: 141677
negative_passages.text: Definition of complex conjugate in complex vector space
negative_passages.docid: 132525
negative_passages.text: Real Numbers Raised to Imaginary Powers?
negative_passages.docid: 24072
negative_passages.text: Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$
negative_passages.docid: 94878
negative_passages.text: Scheme: Changing the definition of complex numbers to accept vectors
negative_passages.docid: 73687
negative_passages.text: Powers of $i$ in Complex Numbers.
negative_passages.docid: 79425
negative_passages.text: Prove the direct product of nonzero complex numbers under multiplication.
negative_passages.docid: 11089
negative_passages.text: For which complex $a,\,b,\,c$ does $(a^b)^c=a^{bc}$ hold?