WhiteningProving de Moivre's Formula for Complex Numbers?

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In summary, the conversation revolves around a homework question involving de Moivre's formula and complex variables. The asker is unfamiliar with the topic and needs help with proving the given equation. They consider using geometric series and de Moivre's formula and are unsure where to start. The responder suggests posting the problem without an image and the asker thanks them for the advice.
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Vitani11
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Homework Statement


Picture has been uploaded with question.

Homework Equations

The Attempt at a Solution



I have literally never seen anything like this in my life. I'm in mathematical physics. I looked up de Moivre's formula and I guess this comes from a course in complex variables? I don't know why this is a homework question given that nobody in my class has actually taken it, but whatever. I need to be able to prove this. Can you please help me out, where should I start? I am familiar with geometric series and I guess I can reference De Moivre's formula. That's where I'm at. My initial thought was that this had something to do with a taylor expansion, but I know cos(x)'s taylor expansion and I don't think that has anything to do with this.
 

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  • #2
Write out de Moivre's formula and see if it has the same form as one of the summands you're given.
 
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  • #3
Vitani11 said:
Can you please help me out, where should I start?
Start by posting an image that is right side up.
 
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  • #4
LCKurtz said:
Start by posting an image that is right side up.

Better still: do not post an image at all; type out the problem (the much preferred PF way).
 
  • #5
Okay.
 
  • #6
Got it, thank you Teeth
 

Related to WhiteningProving de Moivre's Formula for Complex Numbers?

What is a summation?

A summation is a mathematical operation that involves adding a sequence of numbers together. It is represented by the symbol Σ (sigma) and is commonly used in mathematics and science to calculate the total of a series of values.

How do you prove a summation?

To prove a summation, you need to show that the sum of the terms in the sequence is equal to the given value. This can be done by using mathematical properties, such as the commutative and associative properties, to rearrange the terms and simplify the expression.

What is the purpose of proving a summation?

The purpose of proving a summation is to ensure the accuracy and validity of the calculation. By proving the summation, you can demonstrate that the result is correct and avoid any errors or miscalculations.

What are some common methods for proving a summation?

There are several common methods for proving a summation, including mathematical induction, direct proof, and proof by contradiction. These methods involve using logical reasoning and mathematical principles to show that the summation is correct.

Why is proving a summation important in scientific research?

In scientific research, it is important to prove summations in order to validate the results and conclusions of a study. By proving the summation, you can demonstrate the accuracy of your findings and ensure that your research is reliable and credible.

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