(a) Carefully state Watson's lemma.

(b) Use the method of steepest descent and Watson's lemma to obtain an infinite asymptotic expansion of the function

$$I(x)=\int_{-\infty}^{\infty} \frac{e^{-x\left(z^{2}-2 i z\right)}}{1-i z} d z \quad \text { as } \quad x \rightarrow \infty$$