complex numbers (1 Viewer)

[jnney]

Find the roots of the equation z^6+z^5+..........+z+1=0. Hence find the exact value of cos2pi/7 + cos4pi/7 + cos6pi/7.


So I got up to this step:

Sum of roots = 2cos2pi/7 + 2cos4pi/7 + 2cos 6pi/7. What should I do next?

Thanks in advanced.

 

[HyperComplexxx]

Sum of root = -1 = 2cos2pi/7 + 2cos4pi/7 + 2cos 6pi/7
Divide errything by 2 then
cos2pi/7 + cos4pi/7 + cos6pi/7 = -1/2

 

[jnney]

Oh my god i made a silly mistake.

thanks!

 

[kayven]

Is this a complex number question which some-what relates to sequences and series?

 

[nightweaver066]

Is this a complex number question which some-what relates to sequences and series?

Nope, just polynomials.