2.1.8 So­lu­tion math­c­plx-h

Ques­tion:

Ver­ify that $\left(e^{{\rm i}\alpha}-e^{-{\rm i}\alpha}\right)$$\raisebox{.5pt}{$/$}$​$2{\rm i}$ $\vphantom0\raisebox{1.5pt}{$=$}$ $\sin\alpha$.

An­swer:

Ap­ply the Euler for­mula for both ex­po­nen­tials and note that $\sin(-\alpha)$ $\vphantom0\raisebox{1.5pt}{$=$}$ $\vphantom{0}\raisebox{1.5pt}{$-$}$$\sin\alpha$.