this post was submitted on 01 Jul 2025
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It is just a definition, but it's the only definition of the complex exponential function which is well behaved and is equal to the real variable function on the real line.
Also, every identity about analytical functions on the real line also holds for the respective complex function (excluding things that require ordering). They should have probably explained it.
She did. She spent a whole class on about the fundamental theorem of algebra I believe? I was distracted though.