Question

\[(1-i)^{1+i}=?\]
\[(1-i)^{1+i}=?\]
@Mathematics

Answer 1

1-i
r = sqrt(2)
theta = -45 -> 315 -> 7pi/4 rad



1+i -> r = sqrt(2)
theta = 45 -> pi/4 rad


((sqrt(2)e^((7pi/4)i)) ^ 1) *(sqrt(2)e^((7pi/4)i))^i)

(sqrt(2)e^((7pi/4)i)) * sqrt(2)e^((7pi/4)i^2))
(sqrt(2)e^((7pi/4)i)) * (sqrt(2)e^(-7pi/4))

Answer 2

now you can turn it again to im re form

Answer 3

The question asks me to find the principal values of the above expression. What have you found? Is it the principal value? If not how to find that,? If you have found the principal value, what are the other values?