Section 1
Bits and Qubits
$$\text { Write } V=\left[\begin{array}{l}3+2 i \\4-2 i\end{array}\right] \text { as a sum of }|0\rangle \text { and }|1\rangle \text {. }$$
$$\text { Normalize } V=\left[\begin{array}{l}15-3.4 i \\2.1-16 i\end{array}\right] \text {. }$$
Exercise 5.1.3 Express the three bits 101 or $|1\rangle \otimes|0\rangle \otimes|1\rangle \in \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$ as a vector in $\left(\mathbb{C}^2\right)^{\otimes 3}=\mathbb{C}^8$. Do the same for 011 and 111 .
What vector corresponds to the state $3|01\rangle+2|11\rangle$ ?