# Invoking Complex Analysis!

Algebra Level 5

If $$\large x_r = \cos \left( \dfrac{\pi}{5^r} \right) + i \sin \left( \dfrac{\pi}{5^r} \right)$$

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 $$|z|$$ denotes the real part, the imaginary part and the magnitude of $$z$$ respectively.

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