The discussion focuses on finding the power series for the expression e^z + e^(ωz) + e^((ω^2)z), where ω is defined as e^(2πi/3). Participants emphasize the importance of utilizing the equation 1 + ω + ω^2 = 0 to simplify the coefficients in the power series. The solution involves writing the series as a sum of (z^n)*(1 + ω^n + ω^(2n))/n! for n from 0 to infinity. Analyzing specific cases for n=0, 1, 2, and 3 is recommended to facilitate generalization of the solution.
PREREQUISITESStudents and educators in mathematics, particularly those studying complex analysis and power series, as well as anyone seeking to deepen their understanding of exponential functions in the context of complex numbers.
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!