*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