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Is i^i real or complex? plz explain

Is i^i real or complex? plz explain

Grade:12

2 Answers

Sanjeev Malik IIT BHU
101 Points
10 years ago

i think it is not possible for this to exist. AS,

let y=i^i taking log both sides

log y= i* log i

log i= log (root(-1))= 1/2* log (-1) which is not defined as log (-1) is not defined.

so it doesnot exist

Akshay Malik
16 Points
10 years ago

it is real.

i^i=e^(i*pie/2)^i                      {as i = cos 0 + i*sin 0 = e^(i*pie/2) }

    =e^(i*i*pie/2)

    =e^(-pie/2) which is real

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