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I want to know what the standard basis is for C. Would it be {(1, 0), (0, 1)}? Any help would be greatly appreciated.

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  • $\begingroup$ Welcome to Math.SE! I left you a hint to get you started, please update the question or respond in comments if you need further guidance. $\endgroup$
    – gt6989b
    May 7, 2020 at 14:45

1 Answer 1

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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.

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