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In $46-60,$ write each quotient in $a+b i$ form.$$\frac{8+2 i}{1+3 i}$$

$=\frac{7}{5}-\frac{11}{5} i$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 5

Operations with Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

McMaster University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:33

In $46-60,$ write each quo…

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01:37

03:10

02:57

01:19

02:29

02:22

02:42

in this problem, we are asked to divide the complex number eight plus two Ah, by the complex number one plus three up. So to simplify this complex fraction, we will need to multiply both the numerator and the denominator by the complex conjugate of the denominator. The purpose of doing this is so that our denominated will cancel out to be a just a real number without an imaginary component. So the complex conjugal of the one plus three eyes one monastery I and we have two most while this body numerator and the denominator. So we're gonna have to foil in both the numerator denominator. So to begin, in the numerator, we have eight times one which is eight. Our outer components are eight and monastery out to give us Mona's 20 fora. And our inner components are two and one, which we're going to give us plus two. Ah, and then lastly, our last components are plus two and monastery on, which is gonna give us monos six squared for our numerator. Now in the denominator, we need to do the same thing. So we have one times one to give us one hour. Outer is monastery out Tom's one, which is minus three. Ah, our interest plus three out Tom's one Nicholas plus three hours and then our last. It's plus three times of Monastery on to give us a modest nine squared. It's okay now, to simplify a little bit. We have These are squares here and square. It is the square root of negative one squared. So each one of these actually a negative one. Now we have minus six. Tom's the negative one, and that is going to work out to be a plus six and then in the denominator, we have modest nine times. Negative one which works out to be a plus, not now. Moving right along. We have eight plus six in the new waiter, which is gonna give us 14. And then we have modest 24 AA plus Chua, which is gonna give us Mona's 22 for our simplified numerator and then in the denominator, we have one hawass non to give us 10 and then modest area. Plus I cancels. So we just have a tent in our denominator. Moving right along. We have 14 monos 22 all divided by 10 but to get our final answer in the A plus B, uh, form. We need to split this fraction apart. So this is actually equal to 14. Over. Chen Monos 22 over 10. Ah, and this could be further simplified to seven over five. Modest 11 over five. Ah, and this is our final incorrect.

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