Q1: Let $\binom{2}{i} \in \mathbb{C}^2$. What is the result after scaling this vector with the factor $2+i \in \mathbb{C}$?

A1: $ \binom{4+2i}{-1 + 2i} $

A2: $ \binom{2+2i}{1 + 2i} $

A3: $ \binom{2+4i}{1 - 4i} $

A4: $ \binom{4}{2i} $

Q2: Consider the vector space $\mathbb{C}^2$ with the standard inner product. What is the result of $\langle \binom{i}{1} , \binom{1}{-i}\rangle$?

A1: $ -2 i $

A2: $ 4 i $

A3: $ i $

A4: $ \sqrt{2} $

A5: $ \sqrt{2} i $

Q3: Consider the vector space $\mathbb{C}^2$ with the standard inner product. Are the two vectors $\binom{1}{i}$ and $\binom{1}{-i}$ orthogonal?

A1: Yes, they are.

A2: No, the inner product is $2$.

A3: No, the inner product is $-2$.

A4: One needs more information.