Establish the identity
(ez)n = enz (n = 0, ±1, ±2, . . .)
in the following way.
(a) Use mathematical induction to show that it is valid when n = 0, 1, 2, . . . .
(b) Verify it for negative integers n by first recalling from Sec. 7 that
zn = (z−1)m (m = −n = 1, 2, . . .)
when z ≠ 0 and writing (ez)n = (1/ez)m. Then use the result in part (a), together with the property 1/ez = e−z (Sec. 29) of the exponential function.