If z and w are two complex numbers such that |zw| = 1 and arg(z) - arg(w) = π/2, then what is z̅w̅?

|z|.|w|=1, z = re^(i(θ + π/2)); w = (1/r)e^(iθ)
z̅w̅ = e^(-i(θ + π/2)).e^(iθ) = e^(-iπ/2) = -i
z̅w̅ = e^(i(θ + π/2)).e^(iθ) = e^(iπ/2) = i