An algebra problem by Soumya Shrivastva

${ \omega }^{ 5 }=1,\quad 1+\omega +{ \omega }^{ 2 }+{ \omega }^{ 3 }+{ \omega }^{ 4 }=0,\quad \left| \omega \right| =1\\ \log _{ 2 }{ \left| \frac { \omega +{ \omega }^{ 2 }+{ \omega }^{ 3 }+{ \omega }^{ 4 }-1 }{ \omega } \right| } =\log _{ 2 }{ \left| \frac { -2 }{ \omega } \right| } =\log _{ 2 }{ \frac { \left| -2 \right| }{ \left| \omega \right| } } =\log _{ 2 }{ \frac { 2 }{ 1 } =1 }$