Simplify[ExpToTrig[ E^(I E^(I Pi/4) - I 3 Pi/4) + E^(I E^(I 3 Pi/4) - I 9 Pi/4)]]

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.