Question: Prove that real-valued complex linear maps are constant (not so for real linear maps) and that nonconstant complex linear maps send open sets to open

Prove that real-valued complex linear maps are constant (not so for real linear maps) and that nonconstant complex linear maps send open sets to open sets (not so for real linear maps).

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To prove that realvalued complex linear maps are constant we first note that a complex linear map between complex vector spaces is a map that satisfie... View full answer

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