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In $26-37,$ find each product.$$(-4-i)(-4+i)$$

17

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 5

Operations with Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

00:59

In $26-37,$ find each prod…

01:28

01:56

01:22

01:16

00:51

00:56

02:03

00:50

Find each product.$$

in this problem. We're asked most with complex number negative for modest by the complex number. Negative for Plus I Now we may notice from the start that these two complex numbers are complex country. It's. But from now we're going to ignore this, and we're going to perform the multiplication as normal. So foiling this out, we have negative four times are negative for which is going to get positive. 16. Our outer opponents are negative for an eye which is going to multiple to get us modest. For I our inner components negative and negative four are going to give us plus for, uh, and then our last components are going to be negative Odd times on to give us a modernist, uh, squared. Okay, now I squared is one because it is the square root of negative one squared. It's okay. Now, keep in mind, we had a mon ist square, so this is actually going to become plus one. Now we have 16 plus one to give us 17 and then we have modest for a plus for which is going to give us plus zero I, which could be further simplified to just 17 now, whenever we are multiplying a complex number by its complex conjugating, there actually is a formula. The formula turns out to be a squared plus B squared where a is the real component and B is the imaginary component. So a Israel and B is imaginary. So in this case, a equaled negative four and be equaled positive one. So if we plug these into this formula, then we're going to get negative four squared, plus positive one squared, which works out to be 16 plus one, which is 17 and that is the answer we got originally.

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