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

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

If z and w are two complex numbers simultaneously satisfying te equations,z^(3)+w^(5)=0 and z^(2)+bar(w)^(4)=1, then

If the complex number z and omega satisfies z^(3)+omega^(-7)=0 and z^(5)*omega^(11)=1 then

Suppose two complex numbers z=a+ib , w=c+id satisfy the equation (z+w)/(z)=(w)/(z+w) . Then

Find the complex number omega satisfying the equation z^(3)=8i and lying in the second quadrant on the complex plane.

Let omega be the complex number cos((2 pi)/(3))+i sin((2 pi)/(3))* Then the number of distinct complex cos numbers z satisfying Delta=det[[omega,z+omega^(2),1omega,z+omega^(2),1omega^(2),1,z+omega]]=0 is

If complex number omega=(5+3z)/(5(1-z))|z|<1 then

Let z be a complex number satisfying (3+2i) z +(5i-4) bar(z) =-11-7i .Then |z|^(2) is