I am trying to prove an exponential identity and am stuck at:
$$\frac{1}{2\pi}\frac{\exp(i(v-w))t}{i(v-w)} |^{a+2\pi}_{a} = 0, \quad \text{for $v \neq w$}$$
The textbook suggests that this is equal because $\exp$ is $2\pi$ periodic which seems clear to me. But wouldn't it also be possible to rewrite this as:
$$\frac{1}{2\pi}\frac{\exp(i(v-w))2\pi}{i(v-w)} = \frac{\exp(i(v-w))}{i(v-w)}$$ ?