examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Algebra
# Roots of Unity

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

If \(w \not= 1\) is an \(n\)-th root of unity, then find the value of

\[ 1+w+w^2+w^3+\cdots +w^{n-1}\]

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Anish Harsha**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

Evaluate

\[ \cos \frac{ \pi}{7} - \cos \frac{ 2\pi }{7} + \cos \frac{ 3 \pi}{7} . \]

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Arpit Dhimanj**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

\[\huge x^{1729}+x^{-1729}\]

Find the value of the above expression if \(x + \frac 1 x = 1 \)

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Shubhendra Singh**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Sanjeet Raria**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

Given \(z^2+z+1=0,\) find the value of

\[\left(z+\dfrac{1}{z} \right)^2+\left(z^2+\dfrac{1}{z^2}\right)^2+\left(z^3+\dfrac{1}{z^3} \right)^2+\cdots+\left(z^{21}+\dfrac{1}{z^{21}}\right)^2.\]

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Sandeep Bhardwaj**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

×

Problem Loading...

Note Loading...

Set Loading...