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Behavior of ComplexExpand

  • To: mathgroup at
  • Subject: Behavior of ComplexExpand
  • From: Levent Kitis <lk3a at>
  • Date: Wed, 4 Aug 93 17:34:27 -0400

Does someone have an explanantion for the discrepancy between
Out[2] and  Out[3]?

In[2]:= ComplexExpand[ Conjugate[ Exp[a I] ] ]

Out[2]= Cos[a] + I Sin[a]

In[3]:= ComplexExpand[ Exp[a I] ]

Out[3]= Cos[a] + I Sin[a]

If a is replaced with a numerical value the same situation persists:

In[6]:= ComplexExpand[ Conjugate[ Exp[2 I] ] ] == ComplexExpand[ Exp[2 I] ]

Out[6]= True

But ComplexExpand works with a little help:

In[10]:= ComplexExpand[ Conjugate[z], {z} ]

Out[10]= -I Im[z] + Re[z]

In[11]:= ComplexExpand[ Conjugate[z], {z}] /. {z -> Exp[2 I]}

Out[11]= Cos[2] - I Sin[2]

and with a symbolic argument a:

In[13]:= ComplexExpand[ Conjugate[z], {z}] /. {z -> Exp[a I]}

Out[13]= -I Im[E^(I a)] + Re[E^(I a)]

In[14]:= ComplexExpand[%]

Out[14]= Cos[a] - I Sin[a]

and this too works:

In[15]:= ComplexExpand[ Conjugate[Exp[a I]], {Exp[a I]}]

Out[15]= Cos[a] - I Sin[a]

In[17]:= ComplexExpand[ Conjugate[Exp[a I]], {a I}]

Out[17]= Cos[a] + I Sin[a]

Why shouldn't In[2] be equivalent to In[17] ? All this in Version 2.0.


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