In Exercises 53–58, perform the indicated operation(s) and write ...

Question

In Exercises 53–58, perform the indicated operation(s) and write the result in standard form.(2 + i)² − (3 − i)²

Accepted Answer

Hello, everyone. We are asked which of the following expressions is equivalent to the parentheses. 12 plus I squared minus the parentheses. Seven minus I squared. A 34 plus 14 I B minus 36 I C 28 plus 42 ID, 95 plus 38. I rewriting my expression in parentheses. We have 12 plus I closed parentheses squared minus the parentheses. Seven minus I closed parentheses squared. I'm gonna square these complex numbers just like if they were binomials. I recall that scoring a binomial I can square the first term. So 12 squared squared, the last term I squared take the product of the two terms of the binomial multiplied together. So 12 I and multiply it by two. So right now I have 12 squared plus I squared plus two multiplied by 12. I, I think I'm gonna simplify this entire expression before I do the second term. So 12 squared is 144 I squared is negative one plus two multiplied by 12. I is 24. I, I'm gonna bring down my minus sign and I'm gonna do out seven minus I squared and I'm gonna keep that in parentheses until I take care of the minus sign I just brought down. So scoring, the first term gives me seven squared. Scoring. The last term gives me I squared. The two multiplied together will be negative seven I and multiplied by two. We'd have negative seven. I multiplied by two. And I'm gonna close those parentheses. I'm keeping the parentheses, but I'm gonna clean up my squares. So seven squared is 49 minus I squared. I'm sorry, plus I squared, which is negative one and then negative seven, I multiplied by two is negative 14. I rewriting the beginning. I'm gonna combine my 144 and my negative one to be plus 24 I and now I'm gonna distribute the negative sign into the parentheses that follow it. So we'll have minus 49 plus one plus 14. I, I will now combine all my like terms that I can. So I have 143 negative positive one. And when I combine those, I get 95 and then 24 I and 14, I will combine to a positive 38. I, so the expression this is equivalent to is 95 plus 38 I which is answer choice. D have a nice day.

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In Exercises 53–58, perform the indicated operation(s) and write the result in standard form.(2 + i)² − (3 − i)²

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