Yes, in Mathematica, you can expand an exponential of a sum using the rule: exp(a+b)=exp(a)⋅exp(b)

For your specific expression Exp[a + b] + c Exp[a + d], you can factor Exp[a] and express it in terms of exponentials of b and d, especially if they are imaginary numbers.

Mathematica Code: mathematica

Exp[a + b] + c Exp[a + d] // Expand (* Output: Exp[a] Exp[b] + c Exp[a] Exp[d] *)

Factor[Exp[a + b] + c Exp[a + d], Exp[a]] (* Output: Exp[a] (Exp[b] + c Exp[d]) *) If b and d are purely imaginary, you can further use trigonometric expansion:

mathematica

ExpToTrig[Exp[I b] + c Exp[I d]] This will convert exponentials of imaginary numbers into sine and cosine terms.

Summary: Use Expand to apply Exp[a + b] → Exp[a] Exp[b]. Use Factor to extract common terms like Exp[a]. Use ExpToTrig to convert exponentials of imaginary numbers into trigonometric functions.