Evaluate x² − 2x + 2 for x = 1 + i.

Question

Accepted Answer

Yeah, hello everyone. We are asked to evaluate the given quadratic expression for X equal to three plus I. The expression is X squared minus six, X plus 10. Our answer choices are A eight B zero C three plus 15 I D negative six plus eight. I, so our expression we are given again was X squared minus six, X plus 10. And we want X to equal three plus I, I'm going to put three plus I in parentheses. And then I'm going to put that into my expression for the X value. So this will give us parentheses three plus I closed parentheses squared minus six, multiplied by the parentheses. Three plus I closed parentheses plus 10. So I know that I need to square the parentheses. Three plus I, I could use foil or I recall that there was a shortcut. Um when I squared a binomial where I could square the first term. So three squared and get nine square, the second term I squared. So plus I squared and then take the product of the two terms in the parentheses. Three I and multiply it by two. So that would be six I, so three plus I in parenthesis, squared equals nine plus I squared plus six. I, you could also use foil. You will get the same result. Next, I'm gonna distribute the negative six into the parentheses. So negative six multiplied by three is negative 18, negative six, multiplied by I is negative six I and then plus 10 didn't change. I'm gonna combine my like terms and I'm gonna substitute negative one in for I squared. As I recall I squared does equal negative one. So I have nine plus negative one and we have a positive six I and a negative six I so that'll cancel out and I then have minus 18 plus 10. So combining my like terms nine minus one is 88 plus negative 18 is negative 10, negative 10 plus 10 is zero. So we did some work and our answer is zero. So answer choice B have a nice day.

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Evaluate x² − 2x + 2 for x = 1 + i.

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