Where again, we are working in the principal branch.
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Thanks. Twitter will use this to make your timeline better. UndoUndo
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No estoy convencido totalmente de que 1^i=1 :/
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In a general branch however, 1 = e^{i*2πn} --> 1^i = 1, e^{-2π}, e^{-4π}...
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Also i^i={exp[i*(pi/2)]}^i=exp[i*i*(pi/2)]=exp(-pi/2)
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Also, i^(-i) = e^(-i(i pi/2)) =e^(pi/2). Which is also real. (-i)^i=e^(i(i 3pi/2)=e^(3pi/2). Which is also real. It seems whenever you have an imaginary base raised to an imaginary power you get a real number. This doesn't hold generally to complex numbers
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