hello, This message is properly read with FIXED fonts. I am working on arguments of complex numbers. For example, arg(1/2^(1/2+12*I) , if you use Maple or Mathematica or by hand you can expand this BUT, actually the expression is quite cumbersome and tricky. The proper answer is 2*Pi - 12*log(2). But that answer does not appear at fist hand, the <12> comes from an operation with { } and [ ]. the same with argument(2^I+3^I), it is a linear combination of log(2) and log(3). Again, the coefficients are coming from [ ] and { } functions. Strange, because if you try to simplify an expression like Arg of 1/2^(1/2+I)+1/3^(1/2+I) which is 1/2 1/2 2 sin(ln(2)) + 3 sin(ln(3)) arctan(---------------------------------) 1/2 1/2 2 cos(ln(2)) + 3 cos(ln(3)) Yes, but the arctan of sin of log should fall back to its feet but in this case it does not. This is tricky, in some very big expression with the Arctan [ Sin [ Log [ ]]] sometimes it does simplify to something more readable and some times not. in the first example the answer once cleaned is : sin(ln(2)) + sin(ln(3)) arctan(-----------------------) cos(ln(2)) + cos(ln(3)) That is the argument of 2^I+3^I which is a linear combination of log(2) and log(3) in disguise. So my question is : why is it that the argument does simplify and why ?? I looked at many trig identities and could not find the reason. Some of the cases where cracked using LLL algorithm and my big table of real numbers, so I cheated. If someone has a clue on that one ? NOTE: just try Arg[ ] with Mathematica, it won't work. In Maple, in some cases you will get an horrible answer and if you try the usual tricks of simplify(); expand(); evalc(); and such, the only thing it will do is inflate the thing to thousands of characters even with the simple one like 2^(1/2+I)+3^(1/2+I). Here is my question can someone find the closed expression of the ARGUMENT of that simple sum ??? Best regards, any answer would help. Simon Plouffe