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