I'm working my way through Shaum's Outline on linear algebra and in it they define a complex number as an ordered pair of real numbers (a,b). So given a real number a, its complex counterpart would be (a,0). Operations of addition and multiplication of real numbers work under the correspondence:(adsbygoogle = window.adsbygoogle || []).push({});

(a,0) + (b,0) = (a + b,0)

(a,0)*(b,0) = (ab,0)

I can follow that, but I'm confused how they definei. I knowi=(-1)^{1/2}. They define it as:

i^{2}=ii= (0,1)(0,1) = (-1,0) = -1

So am I to assume that any complex number written as (0,b) = -b?

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# Complex Numbers in Linear Algebra

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