Solving a complex equation with Solve

I would like to solve:

$ e^{-b (1.365)} + e^{-b(-0.350)} + e^{-b(-0.378)} = 0$ , where $ b$ is complex.

So, I have written:

Solve[{E^((-b1 - I b2) (1.365)) + E^((-b1 - I b2) (-0.350)) + E^((-b1 - I b2) (-0.378)) == 0, {b1, b2} \[Element] Reals}, {b1,b2}] 

which returns a huge list. How can I get a exact answer? And if it has many solutions, is it possible that I plot the solution points altogether in the complex plane?