I want to know what the standard basis is for C. Would it be {(1, 0), (0, 1)}? Any help would be greatly appreciated.
2026-05-05 13:41:08.1777988468
Give Matrix Representation of the linear function g : C → C given by g(x + yi) = x − yi
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HINT
Yes, the standard basis for $\mathbb{C}$ is indeed $\{1,i\}$ which in matrix notation would be (considering $\mathbb{C} = \mathbb{R}^2$ $$ \left\{ \begin{bmatrix} 1\\ 0 \end{bmatrix}, \begin{bmatrix} 0\\ 1 \end{bmatrix} \right\} $$
The linear function $g:\mathbb{C} \to \mathbb{C}$ will have a $2 \times 2$ matrix $G$ associated with it. Think about what $G$ must do to $1$ and to $i$ and write the matrix representation based on that.