1
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FullSimplify[B^4 + A^3 E^(-I α) Conjugate[
AE^(-I α)], α ∈ Reals && A ∈ Reals && B ∈ Reals]

I recently have the problem of simplifying a complex-valued expression in mathematica. For instance, the result of the above formula should be A^4+B^4. However, because of the annoying complex conjugate. It does nothing and still shows:

B^4 + A^3 E^(-I α) Conjugate[AE^(-I α)]
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  • 1
    $\begingroup$ need space between A and E $\endgroup$
    – kglr
    Mar 2 '20 at 6:50
  • $\begingroup$ OK, I have modified it. $\endgroup$ Mar 2 '20 at 6:53
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First Point is that AE should be A E because otherwise AE becomes a separate variable. Secondly use ComplexExpand.

i.e.

In[3]:= Simplify[
 B^4 + A^3 E^(-I α + I Conjugate[α]) Conjugate[A]]

Out[3]= B^4 + A^3 E^(-I (α - Conjugate[α])) Conjugate[A]

In[4]:= ComplexExpand[%]

Out[4]= A^4 + B^4
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