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Question Number 92453 by jagoll last updated on 07/May/20
(( i))^(1/(i  ))  ?
$$\sqrt[{\mathrm{i}\:\:}]{\:\mathrm{i}}\:? \\ $$
Commented by john santu last updated on 07/May/20
i = e^((πi)/2)  ⇒ (( i))^(1/(i  ))  = (e)^(((πi)/2)×(1/i))  = e^(π/2)    or (√e^π ) = 4.810477381
$${i}\:=\:{e}^{\frac{\pi{i}}{\mathrm{2}}} \:\Rightarrow\:\sqrt[{{i}\:\:}]{\:{i}}\:=\:\left({e}\right)^{\frac{\pi{i}}{\mathrm{2}}×\frac{\mathrm{1}}{{i}}} \:=\:{e}^{\frac{\pi}{\mathrm{2}}} \: \\ $$$$\mathrm{or}\:\sqrt{{e}^{\pi} }\:=\:\mathrm{4}.\mathrm{810477381}\: \\ $$
Commented by mathmax by abdo last updated on 07/May/20
=(i)^(1/i)  =(e^((iπ)/2) )^(1/i)  =e^(π/2)  =(√e^π )
$$=\left({i}\right)^{\frac{\mathrm{1}}{{i}}} \:=\left({e}^{\frac{{i}\pi}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{{i}}} \:={e}^{\frac{\pi}{\mathrm{2}}} \:=\sqrt{{e}^{\pi} } \\ $$

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