Question

Let z be a non-real complex number which satisfy the equation z^(11)=1 then find sum_(k=1)^(10)(1)/(1z^(kua)+z^(k)))

Answer 1

Answer:

The given equation is z

2

+z+1−a=0

If the solution is not real then Δ=b

2

−4ac of the quadratic ax

2

+bx+c=0 is less than zero.

⇒1−4(1−a)<0

⇒1−4+4a<0

⇒4a<3

⇒a<

4

3

Hence, all values of a less than

4

3

will give non-real solutions.