[PDF] set of complex polynomials

How do you find the polynomial of a complex variable?

ij(z z 0)i(w w 0)j. A function of one complex variable looks like a polynomial: f(z) = zng(z). In particular, its zero set agrees with the zero set of a polynomial. Similar statements hold in C2, but we must allow polynomials with analytic coecients.

What is the set of all polynomials?

For example, the set of all polynomials is a function space that does not have a finite dimension; each polynomial can be assigned coordinates by the coefficients of the variables. If you allow power series instead of just polynomials, then you get the space of all analytic functions.

How to find complex zeros of a polynomial function?

Use the Fundamental Theorem of Algebra to find complex zeros of a polynomial function. The Rational Zero Theorem helps us to narrow down the list of possible rational zeros for a polynomial function. Once we have done this, we can use synthetic division repeatedly to determine all of the zeros of a polynomial function.

What are complex roots of a polynomial?

Complex roots of a polynomial The number of roots in a polynomial is equal to the degree of that polynomial. For example, in quadratic polynomials, we will always have two roots counted by multiplicity. These roots could be real or complex depending on the determinant of the quadratic equation.