FP2 de Moivre's theorem issues

ImageUploadedByStudent Room1468162156.769421.jpg

Hi,

I don't understand the last lines of both part k) and part l) in the attached image. Why does the sign change?
Shouldn't it remain positive, or am I missing something fundamental?

I understand that it is Cos(5x--6x) + iSin(5x--6x), but shouldn't it become Cos(11x) + iSin(11x) rather than Cos(11x) - iSin(11x)?

The text book answers has the same result as the image attached, too. What am I doing wrong?

Reply 1

M14B

18

Original post by JLegion

Hi,

I don't understand the last lines of both part k) and part l) in the attached image. Why does the sign change?
Shouldn't it remain positive, or am I missing something fundamental?

I understand that it is Cos(5x--6x) + iSin(5x--6x), but shouldn't it become Cos(11x) + iSin(11x) rather than Cos(11x) - iSin(11x)?

The text book answers has the same result as the image attached, too. What am I doing wrong?

I wish I remembered to help you :frown:

Reply 2

JLegion

OP

2

The text book question was:
(Cos5x + iSin5x) / (Cos3x - iSin3x)^2

The first two lines in the attached image also appear to be mistakes as well.

Reply 3

oShahpo

20

The whole answer is wrong.
(cos3x + isin3x)^2 != (cos(-3x) + isin(-3x))^2

Pretty sure the answers are wrong, both of them, their working out is really dodgy.

Use the fact that

cos(x)+isin(x)=e^{ix}[br]Cos(-x)=cos(x)[br]-sin(x)=sin(-x)

And solve them using exponentials

(edited 7 years ago)

ImageUploadedByStudent Room1468166258.475719.jpg144.8KB

Reply 5

B_9710

18

Maybe its easier to write it in exponential form and you can just think of it as laws of indices.

Reply 6

Maetras

9

Original post by JLegion

Hi,

I don't understand the last lines of both part k) and part l) in the attached image. Why does the sign change?
Shouldn't it remain positive, or am I missing something fundamental?

I understand that it is Cos(5x--6x) + iSin(5x--6x), but shouldn't it become Cos(11x) + iSin(11x) rather than Cos(11x) - iSin(11x)?

The text book answers has the same result as the image attached, too. What am I doing wrong?

The edexcel textbook for each unit has so many mistakes it's actually a joke. One mistake I came across was that they couldn't even calculate tan49 or something like that. I stuck to past papers and madasmaths.

Reply 7

Ayman!

15

The book's working looks dodgy, I don't think it's right.

\displaystyle z=\frac{e^{-i\theta }}{\left ( e^{-2i\theta } \right )^{3}}=e^{-i\theta -\left ( -6i\theta \right )} \iff z= \cos5\theta + i \sin 5\theta

Reply 8

JLegion

OP

2

I'm glad I'm not in the wrong. Normally I would assume the textbook was false, but due to both Edexcel & PhysicsAndMathsTutor getting both part k) and l) different to me, I naturally was very doubtful.
I appreciate all the responses!

FP2 de Moivre's theorem issues

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you