In fact I already tried both 1. and 2. right after posting to math-fun, and there was no improvement! —Dan Gareth McCaughan wrote: ----- On 23/10/2020 22:36, Dan Asimov wrote:

I tried to submit this to Wolfram Alpha in correct syntax, but it never gave any indication that it had the vaguest idea that this was an equation to solve, no less the correct equation to solve for real numbers u, v, w.

Solve[Exp[I(3u+v)] + Exp[I(3v+w)] + Exp[I(3w+u)] == 0, {u,v,w}, Reals]

What am I doing wrong?

I don't know how helpful the following is, but: 1. If I put exactly that into Mathematica, it complains about the instances of I, on the grounds that if you're trying to solve an equation over the reals then all the constants involved must be real. 2. If I replace it with Cos[...]+...==0 && Sin[...]+...==0, then instead I get "The system cannot be solved with the methods available to Solve." -----