SAT Math Part 15 - Simplifying Complex Imaginary Numbers - Free Educational videos for Students in K-12

SAT Math Part 15 - Simplifying Complex Imaginary Numbers - By The Organic Chemistry Tutor

Transcript


00:00	52 . Which is the following is equivalent to the
00:04	expression shown below . So now we're dealing with imaginary
00:08	numbers . Let's begin by distributing the negative sign .
00:13	So this is eight plus five I minus four I
00:18	squared . And then the two negative signs will make
00:22	the next term positive . So this is gonna be
00:24	plus seven I . And then plus five . Now
00:30	let's combine like terms . So we can add these
00:33	28 plus five is 13 . Next we can combine
00:39	size I and 79 That's going to be 12 .
00:44	I . Now what is I squared I . Is
00:51	the square root of negative one I squared . Is
00:54	going to be the square root of negative one squared
00:57	which is negative one . So negative four I squared
01:02	is negative four times negative one which becomes positive for
01:08	Yeah . So now let's add these two numbers 13
01:11	and four 13 plus 4 17 . So that's we
01:17	have the answer 17 plus 12 . I answer choice
01:22	C . Number 53 . What is the product of
01:28	the complex numbers three plus four I . & 5
01:32	-2 . i . The product tells us that we
01:38	need to multiply these two complex numbers . Yeah so
01:43	let's foil . We have 3-plus 5 which is 15
01:50	. And then three times negative two . I That's
01:54	-6 i . And then four times 5 That's gonna
02:00	be 20 i . And then four i . times
02:03	negative two i . Which is negative eight I squared
02:09	. Now our next step is to combine like terms
02:14	-6 . I plus 20 I . That's going to
02:17	be 14 I and I squared I . Is the
02:23	square root of negative run . So I squared is
02:26	going to be the square root of negative one squared
02:30	which becomes negative one . So negative eight I squared
02:36	is negative eight times negative one . So this becomes
02:40	15 plus 14 I plus eight . So let's add
02:47	those two numbers . 15 plus eight is 23 .
02:54	So it's gonna be 23 plus 14 I . Which
02:58	corresponds to answer choice D . 54 . Which of
03:04	the following is equivalent to the expression shown below .
03:09	So in this problem we are dividing two complex numbers
03:14	. We're dividing two plus three I By five plus
03:17	2 . i . So how can we do this
03:22	? In order to simplify this expression ? We need
03:25	to multiply the top and the bottom by the conjugate
03:29	of the denominator . So what is the conjugate of
03:35	the economy ? It's going to have a five .
03:40	It's going to have a to I . But instead
03:44	of the positive sign , we're going to use a
03:47	negative sign . Now at this point , what we
03:52	wanna do is for you . So let's multiply two
03:55	times five which is 10 and then two times negative
03:59	two . I that's going to be negative four I
04:01	. And then three items 5 Which is 15 i
04:06	. And then three times negative two , Yvette's negative
04:08	six I squared on the bottom . Let's do the
04:12	same thing . So we have five times five which
04:15	is 25 , five times negative two i . And
04:19	then two items 5 . And then to I times
04:23	negative two I squared , which is negative for I
04:26	squared . Next let's combine like terms , We can
04:31	add those two and negative 10 . I plus 10
04:33	. I will cancel negative four plus 15 . That's
04:38	going to be positive 11 . And we have negative
04:41	six I squared I squared is -1 . So negative
04:45	six times negative one is positive six . Now negative
04:51	four I square . That's negative four times negative one
04:55	. So this will be positive for Yeah . Now
05:01	10 plus six is 16 And 25 plus four is
05:06	29 . Now we need to put the answer in
05:10	a plus B format . That's in standard form ,
05:13	A . Is a real number , B . I
05:15	. Is the imaginary part of the complex number .
05:19	So we're gonna divide each number by 29 . So
05:23	we're gonna have 16 divided by 29 And then 11
05:27	divided by 29 times i . So we can see
05:31	that answer choice . D . Is the right answer
05:35	number . 55 simplify What is I raised to the
05:40	to 83 equal to ? Well , there's some things
05:46	that we need to know before we could find the
05:48	answer . I is equal to the square root of
05:53	-1 . And we know that I squared this is
05:57	equal to OK . That to just doesn't look right
06:01	, let's do that again . I squared is negative
06:03	one . I . Q . Is going to be
06:06	I squared times I . So this is negative one
06:11	times I are simply negative I . I . to
06:15	the 4th power is I squared squared . So that's
06:21	negative one squared which is one . So to summarize
06:26	it , here's what we have . I . is
06:29	the square root of -1 . I squared is equal
06:33	to -1 . I to the third is negative I
06:38	and I to the fourth is one . But we're
06:43	going to show the work for every step . Just
06:47	keep that in mind . Mhm . So what we
06:51	can do is break down to 83 into 280 plus
06:57	tree . Next Let's divide to 80 x four ,
07:03	28 , divided by 4 7 . So to 80
07:06	, divided by four is 70 . So we can
07:09	write this as I to the 4th raised to the
07:13	to 80 . I mean to the 70 power Because
07:18	four times 70s to 80 I . Q . I'm
07:21	gonna write that as I square times I now I
07:26	to the fourth I'm going to write it as I
07:29	squared squared . Yeah , I squared is -1 .
07:43	So this is what we now have . This is
07:48	for those of you who want to show the work
07:50	for every step . Now negative one squared is positive
07:55	one and negative one times I is negative . I
08:03	1 to the 7th power is still one . So
08:07	this is one times negative I , which gives us
08:10	a final answer of negative I so B is the
08:14	correct answer .

Summarizer

DESCRIPTION:

OVERVIEW:

SAT Math Part 15 - Simplifying Complex Imaginary Numbers is a free educational video by The Organic Chemistry Tutor.

This page not only allows students and teachers view SAT Math Part 15 - Simplifying Complex Imaginary Numbers videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.