finding relationship by using "comparing coefficient" method?????? PLEASE HELP (1 Viewer)

[coeyz]

now we know:

z^5 -1 / z-1 = (Z^2 - 2z cos 2pie/5 +1 ) (z^2 - 2zcos 4pie/5 +1)

we need to show:

cos2pie/5 + cos4pie/5 = - 1/2
AND
cos2pie/5 x cos4pie/5 = -1/4

How to use the comparing coefficient method?
and besides this method, any other ways to use?
THANKSSSSSSSSSSS!!!!!!!!!!

 

[Timothy.Siu]

now we know:

z^5 -1 / z-1 = (Z^2 - 2z cos 2pie/5 +1 ) (z^2 - 2zcos 4pie/5 +1)

we need to show:

cos2pie/5 + cos4pie/5 = - 1/2
AND
cos2pie/5 x cos4pie/5 = -1/4

How to use the comparing coefficient method?
and besides this method, any other ways to use?
THANKSSSSSSSSSSS!!!!!!!!!!

equate coefficients of z, 1=-2cos 2pi/5-2cos 4pi/5
divide by -2, cos 2pi/5+cos 4pi/5=-1/2

sub in z=i
1=(-2icos 2pi/5)(-2icos 4pi/5)=-4 cos 2pi/5 cos 4pi/5

therefore cos 2pi/5 cos 4pi/5=-1/4

 

[coeyz]

wow thanks a lot
is this the standard method of doing it?

so whenever we need to prove sth like,

cos something + cos something = something
We always equating the "z" on both side.

cos something x cos something = something
we always sub z = i to get the answer

am i correct?

 

[Drongoski]

Coeyz . . note that:

 

[Timothy.Siu]

wow thanks a lot
is this the standard method of doing it?

so whenever we need to prove sth like,

cos something + cos something = something
We always equating the "z" on both side.

cos something x cos something = something
we always sub z = i to get the answer

am i correct?

yeah i guess so, but be careful incase theres something different