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Behavior of ComplexExpand
*To*: mathgroup at yoda.physics.unc.edu
*Subject*: Behavior of ComplexExpand
*From*: Levent Kitis <lk3a at kelvin.seas.virginia.edu>
*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.
Levent
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