The discussion revolves around finding the power series for the expression e^z + e^(ωz) + e^((ω^2) z), where ω is defined as the complex number e^(2πi/3). Participants are exploring the properties of complex numbers and power series in the context of this problem.
The discussion includes various approaches to simplifying the series, with some participants providing hints and suggestions for examining specific cases (n=0,1,2,3) to aid in generalization. There is an acknowledgment of the complexity involved in the simplification process.
Participants are working under the constraints of a homework assignment, which may limit the types of guidance they can receive. There is an emphasis on understanding the implications of the equation 1 + ω + ω^2 = 0 in the context of the power series.
rainwyz0706 said:I can write it as the sum of (z^n)*(1+w^n+w^2n)/n!, n from 0 to infinity. But I'm still not sure how to simplify 1+w^n+w^2n from 1+w+w^2=0. Could you explain it in a bit more details? Thanks a lot!