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In $46-60,$ write each quotient in $a+b i$ form.$$\frac{10-5 i}{2+6 i}$$

$\frac{2-6 i}{2-6 i}$$(a+b)(a-b)=a^{2}-b^{2}$$i^{2}=-1$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 5

Operations with Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Oregon State University

Baylor University

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01:32

In mathematics, the absolu…

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In $46-60,$ write each quo…

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all right, so we want to rewrite this quotient in standard form. And the first thing I would see is that we could factor of five out of the top five times a quantity to minus I, and we can factor two out of the bottom two times a quantity one plus three I and that will make the next steps a little bit easier. So the next thing we want to do is multiplied by a special form of one. The conjugated of one plus three. I that would be one minus three I because that's going to simplify the denominator quite a bit. So here's what we have. Now we have the five over to We'll just leave that out and then we're going to multiply using the foil technique first outside, inside last, and we end up with two minus six. I minus I plus three. I squared over same thing on the bottom. First outside, inside last. But because we're multiplying congregates the outsides and insides will cancel. So first will be one and then last will be minus nine. I squared. Okay. There's a lot we can do to simplify. First of all, we have negative. Six i and negative one. I will add those together and get negative. Seven I and every time we have a nice squared will replace it with negative one. So here's what we have now. Five halves times Tu minus seven I plus three times negative. One over one, minus nine times negative one. Let's simplify that a little more. We have five halves times Tu minus seven. I minus three over one plus nine and then let's combine like terms two and negative three. So we have five halves times negative. One minus seven I over 10. Okay, let's go ahead and reduce the five and 10. That gives us a two on the bottom in a one on the top. So what we have at this point is negative one minus seven I over four. And then if we want to break that down into two separate parts, the rial part would be negative. 1/4 and the imaginary part would be plus 7/4. I

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