Complexity Is Awesome!

Algebra Level 5

The equation \(x^{10}+(13x-1)^{10}=0\) has \(10\) complex roots: \(r_1, \overline{r_1}, r_2, \overline{r_2}, r_3, \overline{r_3}, r_4, \overline{r_4}, r_5, \overline{r_5},\) where the bar denotes complex conjugation. Evaluate the expression below.

\[\dfrac 1{r_1\overline{r_1}}+\dfrac 1{r_2\overline{r_2}}+\dfrac 1{r_3\overline{r_3}}+\dfrac 1{r_4\overline{r_4}}+\dfrac 1{r_5\overline{r_5}} \]

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.