Find the real part of `(1-i)^(-i)dot`

Explanation

Let `z= (1-i)^(-i)`. Taking log on both sides, we have
log `z = -I log_(e) (1-i)`
`= -I log_(e)(sqrt(2)(cos.(pi)/(4)- i sin.(pi)/(4)))`
`= - log_(e) (sqrt(2)e^((-ipi//4)))`
`=-i[(1)/(2)log_(e)2 + log_(e) ^(-ipi//4)]`
`= -i[(1)/(2)log_(e),2-(pi)/(4)]`
`= -(i)/(2)log_(e)2-(pi)/(4)`
`rArr z=e^(-pi//4)e^(-i(log2)2)`
`rArr " "Re(Z) = e^(-pi//4) cos((1)/(2) log2)`