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Find number of values of complex numbers `omega` satisfying the system of equaltion `z^(3)=-(bar(omega))^(7)` and `z^(5).omega^(11)=1` |
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Answer» Correct Answer - 2 `(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` |
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