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FP2 De Moivre's Theorem watch

1. Suppose z = cosx + isinx, express cos4x in terms of z

No idea what i am doing.

i thought this question was asking me to write it in terms of cosx

So i have cos^4(x) - 6cos^2(x)sin^2(x) + sin^4(x)

Absolutely lost, pls help.
2. You can put the sin^2(x) in terms of cos^2(x) using C2 trig identities. The sin^4x is similar except you need to square the identity. Sorry for not giving the identity, I think I have to only give hints XD
3. (Original post by BinaryJava)
You can put the sin^2(x) in terms of cos^2(x) using C2 trig identities. The sin^4x is similar except you need to square the identity. Sorry for not giving the identity, I think I have to only give hints XD
Hiya, i have simplified it to 8cos^4(x) - 8cos^2(x) + 1

This is my maximum
4. (Original post by Bobjim12)
Hiya, i have simplified it to 8cos^4(x) - 8cos^2(x) + 1

This is my maximum
Yeah that is what I got. Do you know if we need to know the proof by induction for de moivres theorem?
5. (Original post by BinaryJava)
Yeah that is what I got. Do you know if we need to know the proof by induction for de moivres theorem?
I don't think so,

the answer is 1/2(z^4 + 1/z^4)............................ ..

There isn't an example in my textbook so i haven't a clue what i am doing..
6. Do you know what, i am stupid. Never mind, i have got it now, thankyou though for trying :^)
7. I guess then you let cos4x = z which is the same as z^4 = cosx. Not sure about where the 8 goes though.
8. (Original post by BinaryJava)
Yeah that is what I got. Do you know if we need to know the proof by induction for de moivres theorem?
For edexcel you do
9. (Original post by BinaryJava)
I guess then you let cos4x = z which is the same as z^4 = cosx. Not sure about where the 8 goes though.
yes i was being silly, thankyou
10. (Original post by Gome44)
For edexcel you do
Damn thought I got away from that induction rubbish, seems simple enough.
11. (Original post by Bobjim12)
Suppose z = cosx + isinx, express cos4x in terms of z

No idea what i am doing.

i thought this question was asking me to write it in terms of cosx

So i have cos^4(x) - 6cos^2(x)sin^2(x) + sin^4(x)

Absolutely lost, pls help.
Note that . How can you then express in terms of (and )?

Now use De Moivre's Theorem to do something similar with

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