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Besides the finite fields (Z, , with p prime, there are other finite fields. These fields are extensionJields of Z,. However, before introducingthem, it is instructiveto take a look at how the field of complex numbers C can be constructed as a field extension from the field of real numbers R Recall that there are several representations for complex numbers. Sometimes it is convenient to use a vector notation, in which a complex number is represented as (a, b). Sometimes it is convenient to use a polynomial notation a bi, where i is taken to be a root of the polynomial x 2 1. However, since there is some preconception about the meaning of the symbol i, we replace it with the symbol a,which doesn t carry the same connotations (yet). In particular, a is not (yet) the symbol for 2/--i-. You may think of a ba as being a polynomial of degree 5 1 in the indeterminate a. There is also a polar notation for complex numbers, in which the complex number is written as a ib = reie for the appropriate r and 8. Despite the differences in notation, it should be borne in mind that they all represent the same number. Given two complex numbers we define the addition component-by-componentin the vector notation (a, b) and (c, d ) , where a , b , c and d are all in R, based on the addition operation of the underlying field R.The set of complex number thus forms a two-dimensional vector space of real numbers. We define hp ocr software download windows 7Apr 7, 2015 · Download this app from Microsoft Store for Windows 10, Windows 8.1. See screenshots, read the latest customer reviews, and compare ratings ... free download ocr scanner software for windows 7 7 Best Free OCR Software Apps to Convert Images Into Text
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