In Exercises 37–52, perform the indicated operations and write th...

Question

In Exercises 37–52, perform the indicated operations and write the result in standard form.(- 3 - √-7)^2

Accepted Answer

Welcome back. I'm so glad you're here. We've got this expression, I'll rewrite it. We've got negative two minus the square root of negative 11. All squared. And we get to rewrite that in standard form. What does that mean? Well, we've got a square root of a negative number, which means we're dealing with complex numbers. And we've got to rewrite that in the standard form for complex numbers, which is A plus B. I. Or in terms of I And I by its definition is the square root of -1. Which makes sense because we've got this square root of a negative number here. So we want to rewrite that in terms of I well, let's start with that. We've got negative two minus. I'm going to rewrite this negative 11. That's the same as negative one times 11. So it's the square root of negative one times 11. Now we see that square root of negative one, which can come out as as we just said, and I So we've got negative two minus I squared of 11. All squared. That's looking much better. We've got just a regular square root of 11. Now we can go ahead and do the squaring here, which means we have to rewrite this as negative two minus I squared of 11 times negative two minus I squared of 11. Now we can just do your standard foiling our firsts here negative two times negative two is four. Our outsides negative two times negative I squared of 11, negative times a negative will be a positive. So that'll be a plus two. I square root of 11. Our insides we've got a negative I squared of 11 times a negative two. So negative times a negative is a positive two. I squirt of 11. And our lasts we've got a negative I squared of 11 times a negative I squared of 11. So negative times negative is a positive I times I is I squared and underneath the square root we've got 11 times 11. And I'm just going to write that as 11 squared. Great. A lot of simplifying and combining that we can do here. So let's start with these like terms. So bring down our four plus two I squared of 11 plus two. I squared of 11. That's like saying now we have four I square root of eleven's so we have four I squared of 11. What else can we do? Alright, this one, this I squared. We know from previous lessons by definition I squared is negative one. And so we can plus negative one times okay, in the square root of 11 squared is going to be 11. Great. We can do this multiplication here, bring that down. So we've got four plus four. I square root of 11 plus negative one times 11 is minus 11. And now we can just combine these like terms four minus 11. That's negative seven plus four I square root of 11. And now this is as simplified as it's going to get this is in standard form you might be saying why we've got to have the at the end, Why isn't the eye at the end? We don't want want to run the risk of sticking that i under the square root accidentally, so we just write it right in front of the square root. So this is in standard form, we look at our answer choices and this matches with answer choice. A well done, we'll catch you on the next one.

In Exercises 37–52, perform the indicated operations and write the result in standard form.(- 3 - √-7)^2

Key Concepts

Complex Numbers

Standard Form of Complex Numbers

Squaring a Binomial

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