Consider a quantum state |𝜓⟩ = 𝑘(2 |0⟩ + 1 + 𝑖|1⟩). Find the value of 𝑘.

Consider a quantum state |𝜓⟩ = 𝑘(2 |0⟩ + 1 + 𝑖|1⟩). Find the value of 𝑘. Compute the density matrix associated with this quantum state.