Use De Moivre's Theorem to prove this:

  • Thread starter Thread starter aanandpatel
  • Start date Start date
  • Tags Tags
    Theorem
Click For Summary

Homework Help Overview

The discussion revolves around using De Moivre's Theorem to prove a trigonometric identity involving complex numbers and the tangent function. The original poster presents a specific equation to demonstrate, noting its relevance to a New South Wales HSC question.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to convert the expression into modulus-argument form but expresses uncertainty about the correctness of this approach. Another participant suggests converting tanθ into sinθ/cosθ as a potential first step.

Discussion Status

Some participants have shared initial steps and transformations, indicating a collaborative effort to explore the problem. The original poster acknowledges the helpfulness of the suggestion, leading to a successful conversion of the expression, although no consensus or final solution has been reached.

Contextual Notes

The problem is framed within the context of a homework assignment, with the stipulation that cosθ ≠ 0, which is an important consideration in the discussion.

aanandpatel
Messages
16
Reaction score
0
Use De Moivre's Theorem to show that for any n greater that equal to 1

(1+itanθ)n + (1-itanθ)n =2cosnθ/cosnθ

where cosθ ≠ 0


I tried to approach this by converting into modulus argument form but wasn't really sure if that was correct. It's a common New South Wales HSC question but I couldn't find a solution anywhere. Help would be greatly appreciated :)
 
Physics news on Phys.org
The first step would be to convert tanθ into \frac{sin\theta}{cos\theta} and work from there.
 
Thanks a bunch - that helped a lot. Converted it into:
[(secθ)(cosθ+isinθ)]^n + [(secθ)(cosθ-isinθ)]^n and it was easy from there.

Cheers!
 
No problem. Good luck with the HSC, I just finished mine :P
 

Similar threads

Z^3-1=0 (express using de moivres theorum)
  • · Replies 10 ·
Replies
10
Views
12K
Complex Roots of Z^n = a + bi: Finding Solutions Using De Moivre's Theorem
  • · Replies 18 ·
Replies
18
Views
3K
Solve de Moivre's Theorem: Sin 3x & Cos 3x
  • · Replies 33 ·
2
Replies
33
Views
5K
Solving Roots of Unity with De Moivre's Theorem
  • · Replies 18 ·
Replies
18
Views
4K
De Moivre's theorem for Individual sine functions. Need help
  • · Replies 15 ·
Replies
15
Views
4K
De Moivre's Theorem: Find Expansion of cos 5θ
  • · Replies 4 ·
Replies
4
Views
9K
Solving z^3 = i using De Moivre's Theorem
  • · Replies 1 ·
Replies
1
Views
3K
Answer: Proving Sums with De Moivre's Theorem
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Proving De Moivre's Theorem for Negative Numbers?
  • · Replies 8 ·
Replies
8
Views
9K
Factoring the equation z^(n)-1=0 where z is a complex number
  • · Replies 13 ·
Replies
13
Views
32K