Asked by Tony
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
Answers
Answered by
Steve
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.