# How to get rid of Conjugate in the result of Simplify? [closed]

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)]

• need space between A and E
– kglr
Mar 2 '20 at 6:50
• OK, I have modified it. Mar 2 '20 at 6:53

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