Lecture Notes on Polynomials
نویسنده
چکیده
Looking at the examples in (2.1), we see that the degree of the first polynomial is 2, the second one has degree 16, etc. A number of operations can be performed with polynomials. Given a polynomial p(z) and a complex number c, the polynomial c p(z) is obtained by multiplying each coefficient in p(z) by c. Given two polynomials p(z) and q(z), their sum is defined by adding the coefficients of corresponding power. Some examples will illustrate these definitions. Given p(z) = z − iz + 1 + 7i and c = 1− i, we have c p(z) = (1− i)(z − iz + 1 + 7i) = (1− i)z + (1− i)(−i)z + (1− i)(1 + 7i) = (1− i)z + (−1− i)z + 8 + 6i. Let q(z) = −z + 4z − 8z − 8. Then the polynomial p(z) + q(z) is given by p(z) + q(z) = (z − iz + 1 + 7i) + (−z + 4z − 8z − 8) = (1 + (−1))z + (0 + 4)z + (−i+ (−1− i))z + (1 + 7i+ (−8)) = 4z + (−1− 2i)z − 7 + 7i.
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تاریخ انتشار 2008