Invoking Complex Analysis!
Algebra
Level
4
If \(x_r = \cos \left( \dfrac{\pi}{5^r} \right) + i \sin \left( \dfrac{\pi}{5^r} \right) \), evaluate the value of:
\[\large \Re\left(\prod_{r=1}^\infty x_r \right) + \Im\left(\prod_{r=1}^\infty x_r \right) + \left|\prod_{r=1}^\infty x_r \right| \]
where \(\Re(z)\), \(\Im(z)\) and \(|z|\) are the real part, imaginary part and absolute value of complex number \(z\).
by
Kishore S Shenoy