If `z+(1)/(z)+1=0, "then" z^(2003)+(1)/(z^(2003))` is equal to

Z is a complex number such that z+(1)/(z)=2cos3^(0), then the value of z^(2000)+(1)/(z^(2000)) is equal to

If z+z^-1=1 ,then z^100+z^(-100) is equal to

If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)

If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)

z is a complex number such that z+1/z=2cos 3^0 ,then the value of z^(2000)+ 1/z^(2000) is equal to

|z|=1&z^(2n)+1!=0 then (z^(n))/(z^(2n)+1)-(z^(n))/(z^(2n)+1) is equal to

Let z_(1) and z_(2) be two given complex numbers such that z_(1)/z_(2) + z_(2)/z_(1)=1 and |z_(1)| =3 , " then " |z_(1)-z_(2)|^(2) is equal to

Let z_(1) and z_(2) be two given complex numbers such that z_(1)/z_(2) + z_(2)/z_(1)=1 and |z_(1)| =3 , " then " |z_(1)-z_(2)|^(2) is equal to