The complex logarithm is a multifunction. If w is a particular logarithm of z ≠ 0, meaning expw = z, then every value of logz has the form w + 2nπ‎i where n is an integer. To define logz as a function, principal values can be chosen via a branch of the logarithm on a cut plane; for example, every z in the complement of [0,∞) can be uniquely written z = rexp(iθ‎), where r>0 and 0<θ‎<2π‎ and we set logz = lnr + iθ‎. This defines a holomorphic function logz on the cut plane, with derivative 1/z but which has a discontinuity of 2π‎i across the cut. Branches of complex powers might then be defined by z^α‎ = exp(α‎logz), which is again holomorphic and has derivative α‎z^α‎–1.