complex number calculation

Evaluate {(1+i)^(1-i)} and describe the set{1^x} when x is a real number, distinguish between the cases when x is rational and when x is rational. for now considering the complex number. i dont know how to start with,for firest part i just write it into e^((1-i)log(1+i)) then get the number with e to the power which inculding i , and the secound part , for 1=e^(i2npi) then 1^x is e^(2inxpi) then how to consider the case for rational and irrational here？？？？？

Re: complex number calculation

Re: complex number calculation

should it be if 1=exp(2ikpi) then 1^x= exp(2ikpix) then consider the rational and irrational case on this form. but whats the differences , i have no idea..

Re: complex number calculation

Re: complex number calculation

i might think thats for rational 1^(p/q) just the q roots of 1 but irrational thats infinite number cause 1^x=exp(2ikpix) then i is infinite many to be chosen