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In $19-34,$ write each sum or difference in terms of $i$$$\sqrt{50}+\sqrt{-2}+\sqrt{200}+\sqrt{-50}$$

$8 i-4$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 4

The Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Campbell University

McMaster University

Lectures

01:32

In mathematics, the absolu…

01:11

00:44

In $19-34,$ write each sum…

01:24

00:58

01:09

00:39

03:33

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01:30

Simplify each sum or diffe…

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Simplify the expression us…

Okay, so this one got just a bit more complicated. So I have a square root of 50 plus a square root of a negative too. Plus the square root of 200 plus the square root of negative 50. And so they want us to combine our like terms and get it into terms of I. So here, this 50 this 50 it's perfect. Square is a 25 in it too. And so same goes for this guy here. And then this one here is a two time The 100 is This is our biggest perfect square. And our negative too, is the smallest it can be. And so here, this has no negative in front of it. So I just take the swear to 25 times a squared it two plus and this one does. So I'm gonna take out that negative and then here, plus the square root of 100 the square root of two, and then hear that negative one I have. So that's that. And then the square root of 25 times the square root of two. So we'll take this guy one step at this time, so I have this turns into a five. So I have five square root, too. And then this here plus sign, I haven't I and a square root of two. And then here I have a 10 and a square root of two. So plus 10 square root, too. And then here's an eye. This is five square to 25 5 in the square root of two stays as it is so, plus, ah five I square root of two. So here we cannot combine this five square to two in the ice core to two because they both need to have that imaginary number so you can see that I can combine those two terms. And then I can combine these two terms. So a five plus a 10 is 15 square root of two, and then a five I plus an eye is plus six I square root of two

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