Write each number in standard form a+bi. -6-√-24 / 2

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression in the numerator we have minus the square root of negative 108. And that's all divided by six. We are to use the standard form of complex numbers to rewrite the expression. Well, what is the standard form of complex numbers? We recall from previous lessons that that is A plus B. I. Where we have all the regular numbers first and then next we have all the numbers that are being multiplied by the eye. But we don't even have an eye in our expression yet. Where would we find that? Well, let's take a closer look at this square root of -108. Let's break that down a little bit. So we could rewrite the square root of negative as negative one times 108. All inside of the radical. And we could break that 108 down. 108 is the same as nine times 12. And we could break that 12 down a bit bringing down the rest 12 is the same as four times three. Now looking at each of these parts individually, we recall from previous lessons that the square root of -1. By definition is I there's ri so we can bring an eye out front. Now the square root of nine is three. So we can bring a three out of the radical and the square root of four is two. So we can bring it to outside of the radical. And that just leaves the square root of three. So we have two times three times I two times three is six. So we've got six I square root of three. All that from the square root of negative 108. So now let's rewrite our numerator. We have 27 minus instead of the square root of negative 108. It's six I square root of three. That's all divided by six. But we need to separate our regular numbers from the ones being multiplied by the eyes. So we can take both time terms in the numerator and divide them by six. So we'll have 27/6 minus six. I squared of 3/6. Now let's simplify what we can for our 27 R six in that first term they're both divisible by three. So we can take 27 divided by three which is 9/6 divided by three which is two minus. Well both of these terms here are divisible by six. So we have six divided by six. That's just one. We don't need to write the one. We can just put i square root of three. So for our final answer we have 9/2 minus I times the square root of three. We look at our answer choices and this matches with answer choice. B Well done. We'll catch on the next one

Write each number in standard form a+bi. -6-√-24 / 2

Key Concepts

Complex Numbers

Standard Form

Simplifying Square Roots of Negative Numbers

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