Why can I ignore the "imaginary" value from the gain of my system?
You can ignore it because it is small, and the error comes because the pole has not been that precisely determined.

With the pole value you give (0.719 + 0.215 j), the solution from the characteristic equation for k is 0.0626793 - 0.0000849631 j. As the precision in the pole value is increased the imaginary part will become even closer to zero.

[I should also add that you are not plotting the polar (Nyquist) plot but rather the root locus plot.]