automorphism

logistic_guy

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Let \(\displaystyle \tau\) be the map \(\displaystyle \tau : \mathbb{C} \rightarrow \mathbb{C}\) defined by \(\displaystyle \tau(a + bi) = a - bi\) (complex conjugation). Prove that \(\displaystyle \tau\) is an automorphism of \(\displaystyle \mathbb{C}\).
 
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To warm up the audience, we are honored to share this information:

An automorphism of a field is a bijective field homomorphism from the field to itself.

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