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

Answer

2

Explanation

`(z^(3))=((bar(omega)^(7)))implies|z|^(3)=|bar(omega)|^(7)` or
`|z|^(15)=|omega|^35`……..i
Again `z^(5).omega^11=1|z|^(5).|omega|^(11)` or `|z|^15|omega|^33=1`……….ii
From i and ii `implies|z|=|omega|=1`
Again `(bar(omega))^35=1/(omega^(33))implies(bar(omega))^(2)=-1=i^(2)impliesomega=i` or `-i`