$i^{i} =$ $i ^i =$ ?

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Answer 1 · 2016-06-25T16:01:53

$i^{i} = 0.20788$ $i^i=0.20788$

Any complex number can be written as

$x + i y = (\sqrt{x^{2} + y^{2}}) e^{i ϕ}$ $x +i y = (sqrt(x^2+y^2))e^{i phi}$ with ${x,y}in RR^2$

where $phi = arctan(y/x)$

then

$(x +i y)^{x+iy} equiv ((sqrt(x^2+y^2))e^{i phi})^{(sqrt(x^2+y^2))e^{i phi}}$

making $x = 0, y = 1$

$i^i = (e^{i pi/2})^{e^{i pi/2}} = (e^{i pi/2})^i = e^{-pi/2} = 0.20788$

i ^i = ii=i ^i = ?