Everyone learns de Moivre's theorem for integer roots and powers of complex numbers. And some learn that non-integer rationals yield multiple results. And some learn that irrational roots/powers have countably infinite solutions. But...
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...I haven't yet learned how to take complex roots of complex numbers.
If anyone's got any pointers to results or resources lmk!1 reply 0 retweets 0 likesShow this thread
Replying to @web3ally
Not a full answer but a cute fact. If you want i^i this is the same as exp(i log i) so you first need to know log i. Note that log(exp(i pi (2n + 1/2))) = log i for any integer n, so exp(-pi (2n + 1/2)) = i^i for any n, i.e. i^i has infinitely many values, all of which are real.
1:41 AM - 28 Feb 2022
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