“multiplication(of complex numbers)”的概念、定义、翻译、参考文献-科学参考

multiplication(of complex numbers)

Mathematics

单词	multiplication(of complex numbers)
释义	multiplication(of complex numbers) Mathematics For complex numbers z₁ and z₂, given by z₁ = a + bi and z₂ = c + di, the product is defined by $z_{1} z_{2} = (a c - b d) + (a d + b c) i .$ In some circumstances it may be more convenient to write z₁ and z₂ in polar form, thus: $\begin{array}{l} z_{1} = r_{1} e^{i θ_{1}} = r_{1} (cos θ_{1} + i sin θ_{1}), \\ z_{2} = r_{2} e^{i θ_{2}} = r_{2} (cos θ_{2} + i sin θ_{2}) . \end{array}$ Then $z_{1} z_{2} = r_{1} r_{2} e^{i (θ_{1} + θ_{2})} = r_{1} r_{2} (cos (θ_{1} + θ_{2}) + i sin (θ_{1} + θ_{2})) .$ Thus ‘you multiply the moduli and add the arguments’.
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