# JEE Advanced 2016 (6)

**Algebra**Level 5

Say a real number \(r\) is repetitive if there exist two distinct complex numbers \(z_{1},z_{2}\) with \(|z_{1}| = |z_{2}| = 1\) and \(z_{1},z_{2}\) is not equal to \({−i,i}\) such that \[z_{1}(z_{1}^{3} + z_{1}^{2} + rz_{1} + 1) = z_{2}(z_{2}^{3} + z_{2}^{2} + rz_{2} +1)\] There exist real numbers \(a,b\) such that a real number \(r\) is repetitive if and only if \(a < r ≤ b\). If the value of \(|a| + |b|\) can be expressed in the form \(\frac{p}{q}\) for relatively prime positive integers \(p,q\). Find \(100p +q\).

Try my set JEE ADVANCED 2016

*Source: OMO Spring 2016*

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.