Find all values complex equation

[alexcc17]

Homework Statement

i^{.5 - i}

Homework Equations

z^c=e^{c log(z)}

z^1/n=exp[(1/n) log(z)], n is in integer

The Attempt at a Solution

letting c=.5-i and z=i so

z^c=e^{(.5-i) log(i)} = e^{.5 log(i)}*e^{-i log(i)}

from the second equation I reduced it to:
i^.5*e^{-i log(i)} but I'm not sure where to go from there since the second known equation doesn't apply to the e^(-i log(i)) part

 

[Dick]

Homework Statement

i^{.5 - i}

Homework Equations

z^c=e^{c log(z)}

z^1/n=exp[(1/n) log(z)], n is in integer

The Attempt at a Solution

letting c=.5-i and z=i so

z^c=e^{(.5-i) log(i)} = e^{.5 log(i)}*e^{-i log(i)}

from the second equation I reduced it to:
i^.5*e^{-i log(i)} but I'm not sure where to go from there since the second known equation doesn't apply to the e^(-i log(i)) part

exp(log(i)*(.5-i)) is a good start. Now figure out what possible values log(i) could have.

 

[alexcc17]

I got it thanks though