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.

(- 6 - √-12)/48

Accepted Answer

Welcome back. I'm so glad you're here. We've got this expression in the numerator, we have negative eight minus the square root of negative 32. And in the denominator we've got 24. We are to simplify it and write it in standard form. Well, standard form, what does that mean? Standard form. When we've got the square root of a negative number, we're dealing with complex numbers and the standard form for complex numbers is A plus B. I. So that's what we're aiming for, meaning that we're going to look at things in terms of I I by its definition is the square root of negative one, which we've got this square root of a negative number. Now let's rewrite that. We've got negative eight minus. Okay, negative 32. That is the same as negative one times 32. So negative eight minus the square root of negative one times 32. All over 24. And now as we just said, this square root of negative one can be rewritten as I. So in the numerator is negative eight minus I square root of 32. We got rid of that negative inside of the square root. All divided by 24. Great, What else can we do? Well, this square to 32. We can break that down a little bit more, spilled a factor three for 32 32 is eight times 418 is two times four. So this is two times four squared. We'll rewrite this, we have negative eight minus I times the square root of two, times four. Square all over 24. And that's really exciting for this. Four squared because the square root of four squared is four. So now we've got negative eight minus four. I squared of 2/24. Well that's looking pretty good. R square root is just a square root of two. What else can we do? We can break this apart because this negative eight and this negative four I squared of two could both be divided by 24. Trying to work this into standard form and get that eye over on the right hand side. So we've got negative 8/ -4. i squared of 2/24. And now we can do some reducing eight and 24 both divisible by eight. So this is 1/3 and four and 24 are both divisible by four. So this is a 1/6. Rewriting this. We've got negative one third minus I squared of 2/6. And this is so close except we need this eye on the right hand side so we're going to scoot that over. So it comes after the regular numbers and we've got negative one third minus squared of 2/6. I we look at our answer choices and this matches with answer choice. C 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. (- 6 - √-12)/48

Key Concepts

Complex Numbers

Standard Form of Complex Numbers

Simplifying Radicals

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