Posted by **Tony ** on Friday, May 24, 2013 at 3:29pm.

If f(x) is a polynomial with real coefficients such that f(4+3i)=31+16i, then f(4−3i)=a+bi. What is the value of a+b

- Complex numbers -
**Steve**, Friday, May 24, 2013 at 4:04pm
f(x) = ax^n + bx^n-1 + ...

f(h+ki) = a(h+ki)^n + b(h+ki)^n-1 + ..

f(h-ki) = a(h-ki)^n + b(h-ki)^n-1 + ...

All of the even powers of i remain unchanged, and all of the odd powers of i change sign. So, the real part is unchanged, and the imaginary part changes sign.

f(4-3i) = 31-16i

## Answer this Question

## Related Questions

- Math - If f(x) is a polynomial with real coefficients such that f(8+8i)=38+9i, ...
- Math (Algebra) - If f(x) is a polynomial with real coefficients such that f(7+5i...
- math - For every positive integer n, consider all monic polynomials f(x) with ...
- Math - Given that the quadratic polynomial f(x)=3x^2+ax+b has real coefficients ...
- calculus--please help!! - I have two questions that I don't understand and need ...
- Math - Factor the polynomial as the product of factors that are irreducible over...
- math - The function f(x)=x4−15x3+81x2−201x+182 has four complex ...
- Maths - There are two complex roots to the quadratic equation z^2 +(1−16i)...
- Maths - The function f(x)=x^4−15(x^3)+81(x^2)−201x+182 has four ...
- mathematics - x,y and z are complex numbers that satisfy the equations x+y+z=2, ...

More Related Questions