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 Author Comment/Response Bill Simpson 05/16/12 1:18pm FullSimplify will get you part of the way. In[1]:= FullSimplify[(a-I b)*E^((-p-I q)*t)+(a+I b)*E^((-p+I q)*t)] Out[1]= 2 E^(-p t)(a Cos[q t]-b Sin[q t]) This measures Mathematica's complexity of that In[2]:= LeafCount[Out[1]] Out[2]= 22 And the complexity of your desired form In[3]:= LeafCount[2Sqrt[a^2+b^2]E^(-p t)Cos[q t+ArcTan[a,b]]] Out[3]= 27 So Mathematica believes what you want is "more complicated" and will not choose your form without application of brute force In[4]:= FullSimplify[(a-I b)*E^((-p-I q)*t)+(a+I b)*E^((-p+I q)*t)]/.a_ Cos[c_]-b_ Sin[c_]->Sqrt[a^2+b^2]Cos[c+ArcTan[a,b]] Out[4]= 2 Sqrt[a^2+b^2]E^(-p t)Cos[q t+ArcTan[a, b]] That gives you what you asked for and check In[5]:= FullSimplify[(a-I b)*E^((-p- I q)*t)+(a+I b)*E^((-p+I q)*t)==Out[4]] Out[27]= True Please check this carefully for any errors URL: ,

 Subject (listing for 'making a transformation') Author Date Posted making a transformation Ed Nowak 05/16/12 05:19am Re: making a transformation Bill Simpson 05/16/12 1:18pm Re: Re: making a transformation Ed Nowak 05/19/12 00:18am Re: Re: making a transformation Ed Nowak 05/19/12 02:14am Re: Re: Re: making a transformation Bill Simpson 05/21/12 00:41am Re: Re: Re: Re: making a transformation Ed Nowak 05/25/12 01:18am Re: Re: Re: Re: making a transformation Ed Nowak 05/25/12 02:23am Re: Re: Re: Re: Re: making a transformation Bill Simpson 05/26/12 10:14pm Re: Re: Re: Re: Re: Re: making a transformation Ed Nowak 05/28/12 7:22pm Re: Re: Re: Re: Re: making a transformation Michael 05/27/12 07:20am Re: making a transformation Ed Nowak 05/18/12 07:25am
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