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MathGroup Archive 1998

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Re: Sqrt Problems



Hi Paul,


> Forgive me if this is a simple question, but I am trying to get  "1" out
> of the following expression and I can't seem to figure out how:
>
>         u = Sqrt[a+I*b/a] * Sqrt[a^2+I*b] / Sqrt[a]
>
> Is there a package I'm missing or something?

Try it with a sheet of paper and a pencil:

        u = Sqrt[a+I*b/a] * Sqrt[a^2+I*b] / Sqrt[a]             (a)

   <=>  u = Sqrt[a+I*b/a] * Sqrt[a*(a+I*b/a)] / Sqrt[a]         (b)

   <=>  u = Sqrt[a+I*b/a] * Sqrt[a] * Sqrt[a+I*b/a] / Sqrt[a]   (c)

   <=>  u = Sqrt[a+I*b/a] * Sqrt[a+I*b/a]                       (d)

                  b
   <=>  u = a + I---                                            (e)
                  a

an this will be "1" only for a=1 and b=0.

But I found that Mathematica isn't able to simplify eq. (a) to eq. (e).

In[4]:= $Version

Out[7]= Microsoft Windows 3.0 (April 25, 1997)

In[5]:= u = Sqrt[a+I*b/a] * Sqrt[a^2+I*b] / Sqrt[a]

              2                 I b
        Sqrt[a  + I b] Sqrt[a + ---]
                                 a
Out[5]= ----------------------------
                Sqrt[a]


In[6]:= FullSimplify[u]

              2                 I b
        Sqrt[a  + I b] Sqrt[a + ---]
                                 a
Out[6]= ----------------------------
                Sqrt[a]


In[7]:= u = Sqrt[a+I*b/a] * Sqrt[a*(a+I*b/a)] / Sqrt[a]

                 I b              I b
        Sqrt[a + ---] Sqrt[a (a + ---)]
                  a                a Out[7]=
-------------------------------
                    Sqrt[a]

In[8]:= FullSimplify[u]

              2                 I b
        Sqrt[a  + I b] Sqrt[a + ---]
                                 a
Out[8]= ----------------------------
                  Sqrt[a]


... but now ...;-)


In[9]:= u = Sqrt[a+I*b/a] * Sqrt[a] * Sqrt[a+I*b/a] / Sqrt[a]

            I b
Out[9]= a + ---
             a


Regards,
        Raymund



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