Re: Sqrt Problems
- To: mathgroup@smc.vnet.net
- Subject: [mg12129] Re: [mg12042] Sqrt Problems
- From: r.hemmerling@hit.handshake.de (Raymund Hemmerling)
- Date: Mon, 27 Apr 1998 01:46:13 -0400
- Organization: Private Site of Handshake e. V.
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