SOLUTION: Evaluate the quadratic function y=x^2-2x+2 at x=1+i

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Question 113001: Evaluate the quadratic function y=x^2-2x+2 at x=1+i
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2-2x%2B2 Start with the given equation


y=%281%2Bi%29%5E2-2%281%2Bi%29%2B2 Plug in x=1+i


y=1%2B2i%2Bi%5E2-2%281%2Bi%29%2B2 Foil


y=1%2B2i-1-2%281%2Bi%29%2B2 Replace i%5E2 with -1


y=1%2B2i-1-2-2i%2B2 Distribute


y=1-1%2B2i-2i%2B2-2 Group common terms together. This step is optional, but I'm trying to show you that everything cancels

y=cross%281-1%29%2Bcross%282i-2i%29%2Bcross%282-2%29 Cancel like terms


y=0 So after canceling, we get this


So when x=1+i, y=0