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anonymous
 one year ago
How do polynomial identities apply to complex numbers?
anonymous
 one year ago
How do polynomial identities apply to complex numbers?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I only need an example for this

Bossvideogamer21
 one year ago
Best ResponseYou've already chosen the best response.1these are pretty indepth questions, but ill try to simplify the ideas. let's start with the last one by definition, a rational expression is any polynomial divided by any polynomial except for zero. For a rational expression to be "closed" under addition, mult, division, and subtraction, the following must apply: A rational expression plus a rational expression is a rational expression A rational expression minus a rational expression is a rational expression A rational expression times a rational expression is a rational expression A rational expression divided by a rational expression is a rational expression let us denote a rational expression as: a(x) / b(x) rational expressions are pretty much like fractions when it comes to adding/sub/mult/div so the following rules apply: ADDITION: a(x) / b(x) + c(x) / d(x) = (a(x) * d(x) + b(x) * c(x)) / (b(x) * d(x)) SUBTRACTION: a(x) / b(x)  c(x) / d(x) = (a(x) * d(x)  b(x) * c(x)) / (b(x) * d(x)) MULTIPLICATION: a(x) / b(x) * c(x) / d(x) = ( a(x) * c(x )) / ( b(x) * d(x) ) DIVISION: ( a(x) / b(x) ) / ( c(x) / d(x) ) = ( a(x) * d(x) ) / ( b(x) * c(x)) In each case we end up with a polynomial divided by a polynomial which satisfies our definition of a rational expression. Thus, rational expressions are closed under addition, subtraction, multiplication, and division. It might take you a while to soak that it, but it's not so bad.

Bossvideogamer21
 one year ago
Best ResponseYou've already chosen the best response.1I think I have time to help with the first one. As you probably know you can write a complex number in the for (a + bi) now, let's look at a polynomial identity. for example, if we have something x^3  64, we know that equals x^3  4^3 and the polynomial identity says that is equal to (x  4)(x^2 +4x + 16) because we know that anything in the form (a^3  b^3) = (a  b)(a^2 + ab + b^2) however, we know that we can use complex numbers to factor x^2 + 4x + 16 by using the quadratic formula after applying the quadratic formula, we get that x = 2 + 2isqrt(3) and x = 2  2isqrt(3)

Bossvideogamer21
 one year ago
Best ResponseYou've already chosen the best response.1if u need anything, just anything at all let me know
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