This discussion focuses on evaluating limits involving complex numbers and functions, specifically the limits of expressions like lim(n → ∞) n*((1+i)/2)^n, lim(z → 0) (sin(z)/z)(1/z^2), and lim(z → e^(iπ/3)) (z - e^(iπ/3))(z/(z^3 + 1)). The first limit is confirmed to be convergent to 0 due to the modulus of (1+i)/2 being less than 1. The second limit can be approached using power series expansions, while the third limit requires factoring and recognizing the 0/0 indeterminate form, which can be resolved using L'Hôpital's rule or power series.
PREREQUISITESStudents and educators in mathematics, particularly those studying complex analysis, calculus, and limit evaluation techniques.
MATHMAN89 said:I think I got it.
I ended up with
(1-i√3)/6
Sound right?? Should be if I did all the calculations right.