Show that 1-1 zi dz = 1 + e-/2 (1 - i), where the integrand denotes the principal branch zi = exp(i Log z) (|z|

Show that
∫1-1 zi dz = 1 + e-π/2 (1 - i),
where the integrand denotes the principal branch
zi = exp(i Log z) (|z| > 0,−π < Arg z < π)
of zi and where the path of integration is any contour from z = −1 to z = 1 that, except for its end points, lies above the real axis. (Compare with Exercise 7, Sec. 42.)