This is Real.pic.twitter.com/E5JQYz39dp
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Note though, when taking powers of complex numbers we have to be careful. Technically, if we don't restrict the range of θ to be [0,2π) then i^i takes on infinitely many values. All of which, however, are real.
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Proof that 𝑖ⁱ is real and equal to exp(-π/2). (Note: we are working in the principal branch of eⁱˣ)pic.twitter.com/OUo4TSJCDk
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Just went through the arithmetic. It's correct. Never seen that way of Eulers relation before..
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Hardly rocket science, after all
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I've come to realize that all exponentiation is related to taylor series, and that these are really not all that suprising when looked at through the lens of infinite sum series in a 2d vector space
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e i etc these are all shorthand notations for infinite sum functions f(x) where x=1
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