If $$\LARGE{\omega}$$is an imaginary $$\LARGE \text{cube root of unity}$$, then the value of $$\LARGE{\color{red}{\cos [(\omega^{17}+\omega^7) \pi + \frac{\pi}{3}].}} \space \space \space \space is .........?$$

Question

blockcolder · Answer

Hint: $$\omega^3=1$$

maheshmeghwal9 · Answer

i know but i didn't gt:(

anonymous · Answer

$\omega^{17}=\omega^2$ and $\omega^7=\omega$

maheshmeghwal9 · Answer

ya i applied this but didn't gt the answr:(

maheshmeghwal9 · Answer

Answer is $$- \frac{1}{2}.$$

anonymous · Answer

$\omega^2=\overline{\omega}$

anonymous · Answer

oops back soon
add up z plus z conjugate and see what you get

maheshmeghwal9 · Answer

ok:)

anonymous · Answer

i think you get -1 
in fact i am sure of it
in any case you only have two choices for omega and one choice for omega plus omega bar

maheshmeghwal9 · Answer

oh i gt the answer.
thanx a lot:)