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In $26-37,$ find each product.$$\left(\frac{1}{5}-\frac{1}{10} i\right)(4+2 i)$$

1

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 5

Operations with Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

01:16

In $26-37,$ find each prod…

00:59

00:51

01:22

02:03

02:14

01:28

00:48

00:56

in this problem. We're asked most by the complex number 1/5 Modest. 1/10 of the complex number four plus two. Uh, so we will perform multiplication as usual, using the foil method. So to begin, we have 1/5 Tom's four, which is going to give us four. It's okay. And then our outer terms are we have 1/5 and we have to Ah, multiplying this together is going to get us to fifths, huh? And then our inner terms, we have modest 1/10 I and we have four. Multiplying them is going to give us modest four chance high in our last terms. Won't negative 1/10 and positive to our We're gonna give us a modernist to over 10 uh, squared. Now I squared is the same thing is negative one because it is the square root of negative one squared. So we have modest to chance times negative one. So, actually, what we can do here is we can forget. The negative one is here and make the 2/10 positive. Now we need to combine our real parts and our imaginary parts. So we have 4/5 and we have plus two chance. So 4/5 is the same thing is a chance. And then we have plus to chance for a real component. And then we have 2/5 Monas for Fitze has shown here. So what we could do is we could rewrite to Fitz a cz four over 10. Uh and then we have Monness 40 Virgin, huh? So for our real component, we have 8/10 plus two chance, which is Jan over 10. And then for our imaginary component, we have four chance. Ah, modest fortune saw, which is zero I and 10 over 10. Plus Cyril, I may be rewritten as simply one, which is final answer.

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