SOLUTION: Find an nth degree polynomial function with real coefficients satisfying the given conditions. n=3; -4 and 6+5i are zeros; f(1)=250 My question is not exactly the answer to this

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find an nth degree polynomial function with real coefficients satisfying the given conditions. n=3; -4 and 6+5i are zeros; f(1)=250 My question is not exactly the answer to this      Log On


   

Question 1053141: Find an nth degree polynomial function with real coefficients satisfying the given conditions.
n=3; -4 and 6+5i are zeros; f(1)=250
My question is not exactly the answer to this problem. My question is what are 'i's, referring to 6+5i, and how they affect the entire problem.
Answer by ikleyn(52925) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find an nth degree polynomial function with real coefficients satisfying the given conditions.
n=3; -4 and 6+5i are zeros; f(1)=250
My question is not exactly the answer to this problem. My question is what are 'i's, referring to 6+5i, and how they affect the entire problem.
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1.  6+5i is the complex number.
    6 is its real part.
    5i is its imaginary part.
    i is that famous complex number ("imaginary unit") which is i%5E2 = -1.

2.  The polynomials with real coefficients all have this remarkable property:
    if  a+bi is the root of such a polynomial, then the so named (so called) conjugate complex number a-bi is the complex root also.

3.  Since you ask such a question (of an introductory level), then I think 
    it might be useful for you to make acquaintance with complex numbers.

    You may use the lessons in this site:

        - Complex numbers and arithmetic operations on them

        - Complex plane

        - Addition and subtraction of complex numbers in complex plane

        - Multiplication and division of complex numbers in complex plane

        - Raising a complex number to an integer power

        - How to take a root of a complex number

        - Solution of the quadratic equation with real coefficients on complex domain

        - Solution of the quadratic equation with complex coefficients on complex domain

        - Solved problems on taking roots of complex numbers

        - Solved problems on arithmetic operations on complex numbers