I completely agree with Soroban’s sentiment in relpy #2, especially for basic undergraduate complex analysis. However, if you know some advanced topics this can be a very useful exercise.
Recall that et=n=0∑∞n!tn,cos(t)=n=0∑∞(2n)!(−1)nt2n,&sin(t)=n=0∑∞(2n+1)!(−1)nt2n+1
If you notice that the cos series is even and sin series is odd. Thus use the exponential series eit. It will separate into the sum of two series giving eit=cos(t)+isin(t).
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