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

Thread starter NEILS BOHR
Start date Jan 9, 2011

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.

Jan 9, 2011

NEILS BOHR

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??

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Jan 9, 2011

Ted Sand

Have you tried using Euler's formula:
e^ix = cosx + isinx

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

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).