Write each number in standard form a+bi. -3+ √-18 / 24

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression in our numerator we have negative five plus the square root of negative 48. And that is all divided by 76. We are to write this using the standard form of complex numbers. That means we want to get it into the format of A plus B. I. So we've got our regular numbers first and then the ones associated with I the more complex ones. Second. So let's do that. Let's start off by taking a closer look at this square root of -48. Let's simplify that. So when we've got the square root of negative we could rewrite that as the square root of we have a negative one times 48 and we could rewrite the part as the same as 16 times three. So now let's take a look a closer look at this first one, the square root of negative one. We know by definition from previous lessons that the square root of negative one equals I. So we can pull an eye out front. We also take a look at this square root of 16. We know that the square root of 16 is four. So we can bring a four out front as well. And that just leaves inside the square root of three. So we can go back and fill that in in our numerator, our numerator now is negative five plus four. I square root of three. All over 76. And now going back to that standard form, we want our regular numbers first. the ones with no eyes. So that will be a negative five divided by 76 1st. Plus this four I squared of three divided by 76 distributing that 76 to both terms in the numerator. And now let's simplify where we can well we can't do any simplification with negative five divided by 76 but both four and 76 are divisible by 44 divided by four is one. So in the numerator we have I squared of three left and 76 divided by four equals 19. So our simplified answer in standard form is negative five 76th plus I squared of three divided by 19. We look at our answer choices and this matches with answer choice. C While done, we'll catch you on the next one.

Write each number in standard form a+bi. -3+ √-18 / 24

Key Concepts

Complex Numbers

Standard Form

Simplifying Square Roots of Negative Numbers

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