Question

I am so confused as to where to even start with this problem:
a, b, c, and d are real numbers. Let α = a + bi, β = c + di, such that α = β2.
Let Q be the set of rational numbers. Let K be a field, such that Q ⊆ K and a, b ∈ K:
K0 ⊂ K1 ⊂ K2 ⊂ ... ⊂ Kr
K = K0
My job is to find r and construct an explicit tower while considering the following:
All [Kj+1 : Kj ] = 2
c, d ∈ Kr
All Ki contain real elements (thus, we can't extend by i).