Write each number in standard form a+bi. 10+ √-200 / 5

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression in the numerator. We have 64 plus the square root of -675. And that's all divided by three. We are to use the standard form of complex numbers to rewrite this expression. What does that mean? We need to get it into this format that we recall from previous lessons A plus B. I. Where we have kind of the regular numbers first. That's our A. And then the ones being multiplied by the I. Come second. So we don't even have an eye yet. Well where would we be finding an eye? Let's take a closer look at this square root of negative 675. Let's break that down a little bit. If we have the square root of negative 675 we could rewrite that as the square root of negative one times a positive 675. And we know that 675 could be rewritten as 25 times 27 And we could rewrite 27 As nine times 3. And now let's take a look at all of these parts broken down a little bit. We recall from previous lessons that by definition the square root of negative one is equal to ay there's our eye. So we can pull an eye out front And taking a look here. The square root of 25, that's five. So we can pull a five out front And the square root of nine. Well that's three. So we can pull the three out front and that just leaves the square root of three is the only thing left in there. We can simplify this three times five that equals 15. So we have 15 I square root of three. And now we can rewrite our numerator, replacing that square root of negative 675. So we'll put 64 plus instead of the square root of negative 675. It's 15 I square root three, all divided by three. And now let's separate these. We can divide both terms in the numerator by three and we'll be able to separate our regular numbers from the ones being multiplied by the eye. So 64 divided by three is the first one plus 15 I squared of three divided by three is the second one. And we can't simplify 64/3. So we leave that one as is but for R and R three those are both divisible by three. So 15 divided by three is five. So it's plus five I squared of three. And that is in standard form and that's as simplified as that one is going to get. So now we look at our answer choices for 64 divided by three plus five, I squared of three. And that matches with answer choice A Well done. We'll catch on the next one

Write each number in standard form a+bi. 10+ √-200 / 5

Key Concepts

Complex Numbers and Standard Form

Simplifying Square Roots of Negative Numbers

Operations with Complex Numbers

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