Question

Question 4
Evaluate f(n) = -3n3 + 5n2 + n + 6 at n = 2
A

82
B

52
C


Simplify (9 + 7i)/(-10 + 8i)

Answer 1

\[f(n) = -3n^{3} +5n^{2} +n+6 \]
To solve for f(n=2), you simply have to plug the number 2 in for every n in the equation:
\[f(n) = -3(2)^{3} +5(2)^{2} +(2)+6 \]
Now you just simplify and add up the terms.
\[f(n) = -3*8 +5*4 +(2)+6 \]
\[f(n) = -24 +20 +(2)+6 \]
I'm sure you can find the answer from there.

Answer 2

For the complex number, \[(9+7i)(-10+8i)\]
you solve this like you would any algebra equation and treat i as a variable at the beginning (spell check?)
\[9*(-10)+9*(8i)+7i(-10)+7i(8i)\]
Simplify
\[90+72i+-70i+56i^{2}\]
now you combine like terms
\[90+2i+56i^{2}\]
now the complex number comes in, remember that \[\sqrt{-1}=i\]
therefore \[i^{2}=(\sqrt{-1})^{2}=-1\]
If you plug that back in for \[i^{2}\] then
\[90+2i+56(-1)\]
simplify once more and you get your answer
\[34+2i\]