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Aszume that €=y-Inkx); and n =X-y, then U_ =0 a1 Xug+unn- 2uM 4 Zu6 X 0 6 1 X ug +Unn 2uf X Xug+umn + 2u0n 3u Xu# +Unn 7u + 2 7u& +Unn 1 Uinux +Un70...

Question

Aszume that €=y-Inkx); and n =X-y, then U_ =0 a1 Xug+unn- 2uM 4 Zu6 X 0 6 1 X ug +Unn 2uf X Xug+umn + 2u0n 3u Xu# +Unn 7u + 2 7u& +Unn 1 Uinux +Un70

Aszume that €=y-Inkx); and n =X-y, then U_ = 0 a 1 Xug+unn- 2uM 4 Zu6 X 0 6 1 X ug +Unn 2uf X Xug+umn + 2u0n 3u X u# +Unn 7u + 2 7u& +Unn 1 Uin ux +Un 70



Answers

$$u^{\prime \prime}+7 u=0$$

So here, working. But I have to one side. So that means I see you. What? And one this side. I would have a lot of one. So really, just less under two, six months. But as this side. Mm. This way. I have. Yeah. Yes. Oh, so, uh

We are given too complex vectors. U and V. So you as the complex vector the components one plus seven I two minus six I and V is the complex vector with components five minus two I three minus four I in part they were asked to find U plus v. So this is simply vector edition. So this is all I have to do is add the components. So we have one plus seven I plus five minus two y and then to minus six. I plus re minus four I. And then we perform edition of complex numbers by simply adding corresponding parts. So we have six plus five I and then five minus 10 I And so this is you possibly okay, then in part B, we're asked to find three. Plus I time of use. This is a scalar applied to a vector. This is the same as we simply multiply each component of you by three plus I. So we get three plus I times one plus seven I and three plus I times two minus six I This is equal to forming complex multiplication three plus 21 I plus I plus seven eyes squared and three times two is six minus 18 I plus two I minus 12. Sorry, Just minus six. I squared. This is the vector three minus seven is negative. Four plus 22 I and six plus six is 12 minus 16 I. So we get the vector Negative. Four plus 22 i 12 minus 16 I then in part C, we're asked to find two i times you plus four plus seven I times V So this is a linear combination of U and V. Well, to i times you plus four plus seven i times v First we distribute the scholars onto the components of the vectors. So we have to I times, Let's see the components of you. This is one plus seven I and then to I times two minus six I plus four plus seven i times the first component of the this is five minus two I and four plus seven I times three minus four I This is equal to If we simplify by performing complex multiplication. This is to I plus 14. I squared and then four I minus 12. I squared. Plus, so this is four times five is 20 minus eight I plus 35 I minus 14. I squared. Yeah, it's the first component. The second component is four times three, which is 12 minus 16 I plus 21 I minus 28. I squared this simplifies to Let's see, this is negative 14 plus two I and 12 plus four I plus the complex vector says 20 plus 14 is 34 and then we have negative eight plus 35 is plus 27 I and then we have 12 plus 28 is 40. The negative 16 plus 21 is five I not performing Vector Edition. I get negative 14 plus two I plus 34 plus 27 I and 12 plus four I plus 40 plus five I, which simplifies to the vector. Well, we have to perform edition of complex numbers, so we simply add corresponding parts. I get 20 plus 29 I and 52 plus nine I. And so the result is 20 plus 29 i 52 plus nine I The book seems to have a different answer, but I'm not sure how they got that. Then, in part D, we're asked to find you dotted with V So recall that for complex factors, the dot product is the product of the components of you with the congregates of the components of the So we have the first component of you, which is one plus seven i times the congregates of five minus two I plus the second component of U two minus six I times the conjugate of three minus four I. So first I'll apply congregations. This is one plus seven I times simply flip the sign of the imaginary part five plus two I plus to minus six I times three plus four i and then foiling. I get C five plus two I plus 35 I plus 14 I squared plus two times three is six plus eight I minus 18 I minus 24. I squared. So that simplifies two. We have five minus 14 plus 24 plus six. This is negative. Nine plus 30 is positive 21 then we have to I plus 35 37 plus eight. I is 45 minus 18. I 35 minus eight is 27. No, Yes, 27 I. So we get 21 plus 27 i Once again, this is different from the answer that, given the book, I'm not sure how they got the answer in the book and finally in part E were asked to find the magnitude of you and the magnitude of V. So the magnitude of you well, this is defined to be the square root of these sums of the of the sum of the square of the module lists of each component. So for you, this is going to be the square root of the module lists of one plus seven I squared, plus the square of the module list of two minus six I. And so this is the square root of the modules of one plus seven night. Well, this is going to be the sum of the squares of the parts of the complex numbers. So we have one squared or one plus seven squared or 49 plus two squared or four plus negative six squared or 36. And so this is the square root of one plus 49 plus four plus 36 is 50 plus 40 or 90. You can just sleep in this form if you want Likewise, the magnitude of V is defined to be the square root of the sum of the squares of the module I of the components. So this is the square root of square of five minus two y in module lists, plus the module s of three minus four. I squared, and once again, the square of the modules of a complex number is the sum of the squares of the parts of the number. So we have 25 plus negative two squared or four plus nine plus 16, and this is equal to see we have 25 plus nine is 34 plus 20 is the square root of 54.

You used to fight toward up by the legs then Bernardo, by no way then don't of you. But do is there the function is Do you get a polar? That play? You're saying off heads, remember, you minus does a square. The blue bless work equals zero. So first we need to find affordable by blacks. It is it's number. You you can go available on its way in Dubai. Yes, into the polar. It's like into course it's W India. No, the real. But publics might as that square, I don't know, but Bill s equal to zero. Who if you take the Lord of your bagel X over, they can sort it like why it would about pick flight in beside heads and w they're quit. Why does available are excellent. It go calls head to w be part of the business. When it looked like a big old it'll be like side. It's a w it do into the parlor explain into pigs. Plus, he did a bar X like in tow calls to w you do notably obey bill like, but it does. They're squared and do Dorda bill by it all y equals zero so no w by no lady if your tape calm and we will get like minus side Head said that you know, eggs. You did a lot of excellent David Obey evil about it perfectly into course, hitching a B minus there quick. Then the partner took was noticeable. That break elicit opiate bagels that function real bigger. Can you play? It is to explain in group Cools it's a number you into report a bill, but music minus was that square and that would a bill by Bill. Is it my life rules that equal Brazil? So, Lord of Real Baby Bill, is it Indo here in the bar Exley finger? Because hated Abreu by just is that square tickle toe bruise that w so Berta blew by those that you could do. Who's that? W door. But you dicks to Pixley course. Heads of embryo minus Does that question

You used to fight toward up by the legs then Bernardo, by no way then don't of you. But do is there the function is Do you get a polar? That play? You're saying off heads, remember, you minus does a square. The blue bless work equals zero. So first we need to find affordable by blacks. It is it's number. You you can go available on its way in Dubai. Yes, into the polar. It's like into course it's W India. No, the real. But publics might as that square, I don't know, but Bill s equal to zero. Who if you take the Lord of your bagel X over, they can sort it like why it would about pick flight in beside heads and w they're quit. Why does available are excellent. It go calls head to w be part of the business. When it looked like a big old it'll be like side. It's a w it do into the parlor explain into pigs. Plus, he did a bar X like in tow calls to w you do notably obey bill like, but it does. They're squared and do Dorda bill by it all y equals zero so no w by no lady if your tape calm and we will get like minus side Head said that you know, eggs. You did a lot of excellent David Obey evil about it perfectly into course, hitching a B minus there quick. Then the partner took was noticeable. That break elicit opiate bagels that function real bigger. Can you play? It is to explain in group Cools it's a number you into report a bill, but music minus was that square and that would a bill by Bill. Is it my life rules that equal Brazil? So, Lord of Real Baby Bill, is it Indo here in the bar Exley finger? Because hated Abreu by just is that square tickle toe bruise that w so Berta blew by those that you could do. Who's that? W door. But you dicks to Pixley course. Heads of embryo minus Does that question


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