Re: Cube root of -1 and 1

*To*: mathgroup at smc.vnet.net*Subject*: [mg90896] Re: Cube root of -1 and 1*From*: lehin.p at gmail.com*Date*: Mon, 28 Jul 2008 07:54:21 -0400 (EDT)*References*: <g6h5fm$h26$1@smc.vnet.net>

On 27 =C9=C0=CC, 10:44, Bob F <deepyog... at gmail.com> wrote: > Could someone explain why Mathematica evaluates these so differently? > > In[53]:= > > (Sqrt[36] - 7)^(1/3) > (Sqrt[36] - 5)^(1/3) > > Out[53]= (-1)^(1/3) > > Out[54]= 1 > > In other words why isn't (-1)^1/3 expressed as -1 ?? > > Thanks... > > -Bob I subscribe to the question. I also do not understand this behavour: In[12]:= (-1)^(1/3)//ComplexExpand Out[12]= 1/2+(I Sqrt[3])/2 In[13]:= FullSimplify[(-1)^(1/3) == 1/2 + (I Sqrt[3])/2] Out[13]= True But: In[14]:= FullSimplify[(-1)^(1/3)==-1] Out[14]= False In[17]:= (-1)^3 Out[17]= -1 In[20]:= FullSimplify[(-1)^3 == -1] Out[20]= True It is contradiction, is not it?