לדוגמא, נחשב: <math>\sin(\frac{\pi}{4}+i)=\frac{e^{i(\frac{\pi}{4}+i)}-e^{-i(\frac{\pi}{4}+i)}}{2i}=\frac{e^{-1+\frac{\pi}{4}i}-e^{1-\frac{\pi}{4}i}}{2i}=</math>
<math>=\frac{e^{-1}(\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i-e(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i}{2i}=\frac{\frac{\sqrt{2}}{2}(\frac{1}{e}-e)+\frac\sqrt{2}}{2}(\frac{1}{e}+e)i}{2i}=\frac{\sqrt{2}}{4}(\frac{1}{e}+e)-\frac{\sqrt{2}}{4}(\frac{1}{e}-e)i</math>