Finding Re (α + α^2 + α^3 + α^4 + α^5)

  • Thread starter NEILS BOHR
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In summary, the formula for finding Re (α + α^2 + α^3 + α^4 + α^5) is Re (α + α^2 + α^3 + α^4 + α^5) = Re (α + α^2 + α^3 + α^4 + α^5). This can be useful in many fields and can be solved by finding the real parts of each term in the complex number and adding them together. Re (α + α^2 + α^3 + α^4 + α^5) can be negative and can also be expressed as the sum of the real parts of each term in the complex number.
  • #1
NEILS BOHR
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Homework Statement


Let alpha = e ^ i8pi / 11 , then find Re ( alpha + alpha ^2 + alpha ^3 + alpha ^4 + alpha ^5).


Homework Equations





The Attempt at a Solution


look i hav reduced the expression to [tex]\alpha[/tex] ([tex]\alpha^5[/tex] -1 ) / [tex]\alpha[/tex]-1

now what to do??:confused:
 
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  • #2
Have you tried using Euler's formula:
e^ix = cosx + isinx
 

1. What is the formula for finding Re (α + α^2 + α^3 + α^4 + α^5)?

The formula for finding Re (α + α^2 + α^3 + α^4 + α^5) is Re (α + α^2 + α^3 + α^4 + α^5) = Re (α + α^2 + α^3 + α^4 + α^5).

2. What is the significance of finding Re (α + α^2 + α^3 + α^4 + α^5)?

Finding Re (α + α^2 + α^3 + α^4 + α^5) can be useful in many fields, including mathematics, physics, and engineering. It is used to find the real part of a complex number, which has many real-world applications.

3. How do you solve for Re (α + α^2 + α^3 + α^4 + α^5) in a complex number?

To solve for Re (α + α^2 + α^3 + α^4 + α^5), you can use the formula Re (α + α^2 + α^3 + α^4 + α^5) = Re (α + α^2 + α^3 + α^4 + α^5). This involves finding the real part of each term in the complex number and adding them together.

4. Can Re (α + α^2 + α^3 + α^4 + α^5) be negative?

Yes, Re (α + α^2 + α^3 + α^4 + α^5) can be negative. The real part of a complex number can be positive, negative, or zero, depending on the values of the coefficients and exponents.

5. Are there any other ways to express Re (α + α^2 + α^3 + α^4 + α^5)?

Yes, Re (α + α^2 + α^3 + α^4 + α^5) can also be expressed as the sum of the real parts of each term in the complex number: Re (α) + Re (α^2) + Re (α^3) + Re (α^4) + Re (α^5).

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