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.

(- 8 + √-32)/24

Accepted Answer

Welcome back. I'm so glad you're here. We've got this expression, I'll rewrite it. We've got negative 10 plus the square root of negative in the numerator, all divided by five. And we are to simplify and rewrite this in standard form. Well, what does that mean? Well, we've got the square root of a negative number, meaning we're dealing with complex numbers. And the standard form for complex numbers is A plus B. I. And we know that i by its definition is the square root of negative one. So when we've got these square root of negative numbers here, we're going to rewrite that in terms of I. So let's get started on that. We've got negative 10 plus. I'm going to rewrite this squared of negative 50 as the square root of negative one, times 50. All divided by five. And now we see that square root of negative one inside which we know is I. So we can bring an eye out in front. Now we've got negative 10 plus I square root of 50. All divided by five. What else can we simplify? Well, in that square root we've got a 50 we can break that down a bit build a factor tree, 54 50 that's five times 10. Well, 10 is five times two. So this is the same as five squared times two. We cannot write that inside. So we've got negative 10 plus I And inside we've got the square root of five squared times two. All divided by five. And this is exciting for that. Five squared anyway because the square root of five squared is five. So now we can rewrite that with a five in front. We've got negative 10 plus now five I squared of two divided by five. And now what do we do that squared of two is looking pretty good. How do we get this more like standard form? Well we can break this apart into these two terms which are both divisible by five. So that'll that'll work nicely. We've now got negative 10 divided by five plus five, I square root of two divided by five. And cool we can do some reducing 10 and five are both divisible by five. So this is now two and 15 and five are both divisible by five. Those are now ones. So we've got negative two for that first term plus I square root of two and that's as simplified as it's going to get. But you might be saying why are we letting the I stay in front when it's supposed to be B. I Well, if we put the eye afterward, it runs the risk of going underneath that square root symbol and we don't want to do that. So we keep the eye in front for this one and we look at our answer choices and that matches with answer choice. C Well done. We'll catch on the next one

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 8 + √-32)/24

Key Concepts

Complex Numbers

Standard Form of Complex Numbers

Division of Complex Numbers

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