Use definition (1), Sec. 33, of zc to show that (−1 + √3i)3/2 = ± 2 √2.
Use definition (1)
zc = ec log z,
where log z denotes the multiple-valued logarithmic function. Equation (1) provides a consistent definition of zc in the sense that it is already known to be valid (see Sec. 32) when c = n (n = 0,±1,±2, . . .) and c = 1/n (n = ±1,±2, . . .). Definition (1) is, in fact, suggested by those particular choices of c.