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AQA FP2 help needed

Having trouble with question 8 on the AQA FP2 January 2012 paper, specifically part c and d. If anyone would be willing to help I would be extremely grateful.
Here's the link: http://filestore.aqa.org.uk/subjects/AQA-MFP2-QP-JAN12.PDF

Thanks

Reply 1

joostan

Original post by IMZL

What have you tried?

Reply 2

IMZL

Original post by joostan

What have you tried?

I haven't gotten far at all really. Only thing I can see is pairing z+1/z and z^2+1/z^2, to get 2cos2π/5 and 2cos4π/5?

Reply 3

IMZL

Original post by joostan

What have you tried?

I just got part c I think. Using part b to multiply out corresponding linear factors( i.e. (z-e^2πi/5)(z-e^-2πi/5)) noticing e^-2πi/5+e^2πi/5=2cos2π/5 and dividing by z^2?

Reply 4

Zacken

For part (d) find w^2 and see how you can write z^2 + z^(-2) in terms of only w and w^2 this should let you get a quadratic in w.

Reply 5

IMZL

Original post by Zacken

For part (d) find w^2 and see how you can write z^2 + z^(-2) in terms of only w and w^2 this should let you get a quadratic in w.

Oh yeah, got it, thanks!

Reply 6

Zacken

Original post by IMZL

I just got part c I think. Using part b to multiply out corresponding linear factors( i.e. (z-e^2πi/5)(z-e^-2πi/5)) noticing e^-2πi/5+e^2πi/5=2cos2π/5 and dividing by z^2?