# Complex Summation 2

Algebra Level pending

For any complex number $$\omega = a+bi$$, $$|\omega|$$ is defined to be the real number $$\sqrt{a^2+b^2}$$. If $$\omega =\cos 40^\circ + \cos 40^\circ$$, then find$$|\omega +2\omega^2 +3\omega^3 + ... + 9\omega^9|^{-1}.$$ Express your answer to the first three decimal places.

This problem is not original.

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