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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 = -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