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gabrielc42 authored Oct 19, 2024
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Expand Up @@ -202,10 +202,19 @@ <h4>what are three solutions to these:</h4>
c1 :: 3
d1 :: 13
it isnt in order, and our scale is constantly growing. continue on with this subseries, a box if u will. apply phyiscal laws and let’s also dicsuss the perturbation of electromagnetic field via flame ore fire:
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ii = 0.207879576... (Here i is the imaginary number sqrt(-1). Isn't this a real beauty? How many people have actually considered rasing i to the i power? If a is algebraic and b is algebraic but irrational then ab is transcendental. Since i is algebraic but irrational, the theorem applies.

i^i is equal to e(- pi / 2 ) and several other values. Consider i^i = e(i log i ) = e( i times i pi / 2 ) . Since log is multivalued, there are other possible values for i^i.
Here is how you can compute the value of i^i = 0.207879576...
1. Since e^(ix) = Cos x + i Sin x, then let x = Pi/2.
2. Then e^(iPi/2) = i = Cos Pi/2 + i Sin Pi/2; since Cos Pi/2 = Cos 90 deg. = 0. But Sin 90 = 1 and i Sin 90 deg. = (i)*(1) = i.
3. Therefore e^(iPi/2) = i.
4. Take the ith power of both sides, the right side being i^i and the left side = [e^(iPi/2)]^i = e^(-Pi/2).
5. Therefore i^i = e^(-Pi/2) = .207879576...

Does this seem familiar?
1/2⁠ + i t

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