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# FP2 de Moivre's theorem issues

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1. 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?
2. (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?
3. 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.
4. The whole answer is wrong.
(cos3x + isin3x)^2 != (cos(-3x) + isin(-3x))^2
5. Pretty sure the answers are wrong, both of them, their working out is really dodgy.

Use the fact that

And solve them using exponentials
Attached Images

6. Maybe its easier to write it in exponential form and you can just think of it as laws of indices.
7. (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.
8. The book's working looks dodgy, I don't think it's right.

9. 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!

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