If f(x) is a polynomial with real coefficients such that f(8+8i)=38+9i, then f(8−8i)=a+bi. What is the value of a+b?
If f(a+bi) = c+di,
f(a-bi) = c-di
So, f(8-8i) = 38-9i
a+b = 27
29 sir
good catch.
To find the value of a+b, we can use the property of polynomials with real coefficients.
Since f(x) is a polynomial with real coefficients, we can conclude that if a complex number is a solution to the polynomial, then its complex conjugate must also be a solution.
So, if f(8+8i) = 38+9i, then f(8-8i) must also be equal to 38+9i.
Hence, the value of a+b is 38+9 = 47.
Therefore, a+b = 47.