Let a complex number `alpha, alpha^11 != 1` be a root of the equation ` z^18 - z^7 - z^11 + 1 = 0`, then identify the correct option :

Let a complex number alpha,alpha!=1, be a root of the equation z^(p+q)-z^p-z^q+1=0,where p ,q are distinct primes. Show that either 1+alpha+alpha^2++alpha^(p-1)=0or1+alpha+alpha^2++alpha^(q-1)=0 , but not both together.

If z is complex root of the equation x^3+1=0 and (1+z)^7 = P+Qz then P + Q is

Let alpha,beta be real and z be a complex number If z^2+alphaz+beta=0 has two distinct roots on the line Re z = 1 , then it is necessary that :

Let alpha,beta be real and z be a complex number. If z^2+alphaz+beta=0 has two distinct roots on the line Re z = 1, then it is necessary that

If one root of the equation z^2-a z+a-1= 0 is (1+i), where a is a complex number then find the root.

If one root of the equation z^2-a z+a-1= 0 is (1+i), where a is a complex number then find the root.

Let alpha,beta be real and z be a complex number. If z^(2)+alphaz+beta=0 has two distinct roots on the line Re. z=1 , then it is necessary that

For a complex number Z, if one root of the equation Z^(2)-aZ+a=0 is (1+i) and its other root is alpha , then the value of (a)/(alpha^(4)) is equal to

For a complex number Z, if one root of the equation Z^(2)-aZ+a=0 is (1+i) and its other root is alpha , then the value of (a)/(alpha^(4)) is equal to