Hey, Thanks very much.

This is the simplified version of final[5]:-.3618033984*exp(-.6180339885*I*t)-.1381966009*exp(1.618033988*I*t)+.3333333332+.6022082513e-1*exp(-2.302775638*I*t)+.1064458415*exp(1.302775638*I*t) the non simplified version has long decimals in it too though. so i'm guessing its just too complex for MAPLE- but in this case shouldn't it say 'Warning: solutions may have been lost'?

There does seem to be a bug with the RealDomain command. This, in MAPLE, has the RealDomain comand surrounding it, but when copied and pasted, or converted to string, that command gets lost- which explains the imaginary solution but is a bit odd.

> fsolve({final[5]*conjugate(final[5]) = 1.0}, {t});
                     {t = -0.6166684213 - 1.471384271 I}

I've tried using the fsolve command and get the same problem with the known solution not turning up. If I put the inequalities in there I get an error message saying it needs equalities. This is very frustrating as it should be obvious that for numerical solutions, as its not 100% accurate, a range of values might be acceptable.