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FP2 Further Complex Numbers

Hi, got TWO questions in my FP2 book, but couldnt find the way to solve it.
photo.JPG
For the first one,i cant prove it. i have no idea what kind of mistakes that i made. The following is my working
photo (1).JPG
For the second one, i can do part a and b by myself, but i dun know how to do part c by using the answer in part b.
Thanks:smile:
Reply 1
Avatar for mathz
mathz
8
for second question write tan theta =x in rhs. now ignoring lhs what does rhs need to equal to match the x^4... equation?
for first question you need to use

(2cosx)^6=(z+1/z)^6

which follows from the following with n=1

z^n=cosnx+isin nx

z^(-n)=cosnx-isin nx

giving z^(n)+z^(-n)=2cos nx

and the above will help when you exapnd (z+1/z)^n
(edited 11 years ago)
Where you wrote (2 lines from the bottom) cos4(θ)=(12cos(4θ)+12) cos^{4}(\theta) = (\frac{1}{2}cos(4 \theta) + \frac{1}{2}) - instead write cos4(θ)=(cos2(θ))2 cos^{4}(\theta) = (cos^{2}(\theta))^{2} then work from there.
Reply 3
Avatar for 041087
041087
OP
2
Original post by mathz
for second question write tan theta =x in rhs. now ignoring lhs what does rhs need to equal to match the x^4... equation?


i still cant get your meaning:s-smilie:
Reply 4
Avatar for 041087
041087
OP
2
Original post by dantheman1261
Where you wrote (2 lines from the bottom) cos4(θ)=(12cos(4θ)+12) cos^{4}(\theta) = (\frac{1}{2}cos(4 \theta) + \frac{1}{2}) - instead write cos4(θ)=(cos2(θ))2 cos^{4}(\theta) = (cos^{2}(\theta))^{2} then work from there.


thanks:smile:

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