SOLUTION: f(x)=4x^3-3x^2+2x-1. Find f(1+2i). Please help me out, I really don't have any idea on what to do!!!

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: f(x)=4x^3-3x^2+2x-1. Find f(1+2i). Please help me out, I really don't have any idea on what to do!!!      Log On

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Question 165291: f(x)=4x^3-3x^2+2x-1. Find f(1+2i). Please help me out, I really don't have any idea on what to do!!!
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Note: it's helpful to remember that i%5E2=-1


f%28x%29=4x%5E3-3x%5E2%2B2x-1 Start with the given function


f%281%2B2i%29=4%281%2B2i%29%5E3-3%281%2B2i%29%5E2%2B2%281%2B2i%29-1 Plug in x=1%2B2i. In other words, replace each "x" with "1+2i"


f%281%2B2i%29=4%281%2B2i%29%5E2%281%2B2i%29-3%281%2B2i%29%5E2%2B2%281%2B2i%29-1 Break up %281%2B2i%29%5E3 to get %281%2B2i%29%5E2%281%2B2i%29


f%281%2B2i%29=4%28-3%2B4i%29%281%2B2i%29-3%28-3%2B4i%29%2B2%281%2B2i%29-1 FOIL %281%2B2i%29%5E2 to get 1%2B4i%2B4i%5E2=1%2B4i%2B4%28-1%29=-3%2B4i


f%281%2B2i%29=4%28-11-2i%29-3%28-3%2B4i%29%2B2%281%2B2i%29-1 FOIL %28-3%2B4i%29%281%2B2i%29 to get %28-3%2B4i%29%281%2B2i%29=-3-2i%2B8i%5E2=-3-2i%2B8%28-1%29=-11-2i


f%281%2B2i%29=-44-8i%2B9-12i%2B2%2B4i-1 Distribute


f%281%2B2i%29=-34-16i Combine like terms.


So the answer is f%281%2B2i%29=-34-16i