Chapter 2.17, Problem 30MP

Write the series for $e^{x(1+i)}$.

Write $1+i$ in the $r{e}^{i\theta }$ form and so obtain (easily) the powers of (1 + i). Thus show, for example, that the $e^x\cos x$ series has no x² term, no x⁶ term, etc., and a similar result for the $e^x\sin x$ series. Find (easily) a formula for the general term for each series.