Z^n + Z^-n identities question (1 Viewer)

[wiliaamnguuyen]

How would you go about solving part b of this question?
(a) If z = cis.(theta), prove that z^n + z^-n = 2cos (n.theta)
(b) Hence express (z+z^-1)^4 in the form A.cos(4.theta) + B.cos(2.theta) + C

For part B I got up to:
(z+z^-1)^4
= (2cos(theta))^4 (From part a)
= (16cos(4.theta)) ....

 

[glittergal96]

You are confusing cos and cis! Your last line is invalid for this reason.

 

[wiliaamnguuyen]

Oh no!!! Thank you so much, such a stupid mistake