Let a,b be real and z be a complex number

• Complex Numbers

Let a,b be real and z be a complex number. If z² + az + b = 0 has two distinct roots on the line Re(z) = 1, then it is necessary that

1. |b| = 1
2. b ∈ (0,1)
3. b ∈ (1,∞)
4. b ∈ (-1,0)

Answer

Let roots be p + iq and p - iq p, q ∈ R

root lie on line Re(z) = 1 , p = 1

product of roots = p² + q² = b = 1 + q²

The correct option is C.