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How do I define f(x)=x(x−1)^2 and compute f(i+2).

 Feb 6, 2016
 #1
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Put in i + 2    for 'x'

(i+2)(i+2-1)^2

(i+2)(i+1)^2

(i+2) (i^2 + 2i + 1)

(i+2)(-1+2i+1)

(i+2)(2i)

2i^2 + 4i  =  4i -2

 Feb 6, 2016
 #2
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Expand the following: f(i+2) = (i-1+2)^2 (i+2) Add like terms. 2-1 = 1: f(i+2) = (i+2) (i+1)^2 (i+1) (i+1) = (i) (i) + (i) (1) + (1) (i) + (1) (1) = i^2+i+i+1 = i^2+2 i+1: f(i+2) = i^2+2 i+1 (i+2) | | | | i | + | 2 | | i^2 | + | 2 i | + | 1 | | | | i | + | 2 | | 2 i^2 | + | 4 i | + | 0 i^3 | + | 2 i^2 | + | 0 i | + | 0 i^3 | + | 4 i^2 | + | 5 i | + | 2: Answer: | | f(i+2) = i^3+4i^2+5i+2

 Feb 6, 2016
 #3
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Answer: | | f(i+2) = i^3+4i^2+5i+2     since i^2 = -1  and i^3 = -1

                           = -i   -4      +5i+2 =  4i-2

 Feb 7, 2016

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