# 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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