The discussion focuses on proving the equation z^n + 1/z^n = 2cos(nθ) using mathematical induction, given that z is a non-real complex number satisfying z + 1/z = 2cos(θ). Participants suggest that treating cos(θ) as a constant simplifies the induction process. The representation of z as e^(iθ) is introduced, which aids in deriving z^n as (cos(θ) + i sin(θ))^n, leveraging Euler's formula for complex numbers.
PREREQUISITESStudents studying complex analysis, mathematics educators, and anyone interested in advanced algebraic proofs involving induction and trigonometric functions.
mikee said:Homework Statement
If z is a non-real complex number such that z+1/z=2costheta, prove that z^n+1/z^n=2cosntheta for any posistive integer n
Homework Equations
I think the process of induction would work, but I am not quite sure how to do that with all of the unknowns, would i just treat costheta as a constant number
The Attempt at a Solution