Find the number of values of complex numbers `omega` satisfying the system of equations `z^(3)==(overlineomega)^(7)` and `z^(5).omega^(11)=1`

Answer

2

Explanation

`(z^(3))=((overline(omega)^(7)))implies|z|^(3)=|overlineomega|^(7)=|omega|^(7)` or
`|z|^(15)=|omega|^(35)` .(i)
Again `z^(5).omega^(11)=1|z|^(5).|omega|^(11)=1` or `|z|^(15)|omega|^(33)=1` .(ii)
from (i) and (ii) `implies|z|=|omega|=1`
again `(overlineomega)^(35)=(1)/(omega^(33))implies(overline(omega))^(2)-1=i^(2)impliesomega=i` or `-i`