How do you test convergence for an infinite series with imaginary coefficients?

[jbowers9]

If you have an infinite series some or all of whose coefficients involve imaginary terms how do you check for convergence?

 

[DavidSmith]

jsut split series into complex and real parts and test convergence for each part

 

[ZioX]

The reals are a subset of the imaginary numbers. Hence just check for convergence in the complex plane.

 

[d_leet]

The reals are a subset of the imaginary numbers. Hence just check for convergence in the complex plane.

I wouldn't say that, because when you say imaginary number there is usually the implication that you are speaking of a number in the form ri where r is a real number. The reals are, however, a subset of the complex numbers.

 

[SiddharthM]

like davidsmith said, split up the series into real and imaginary parts. Then you effectively have to deal with two real-valued series.