A Complex Infinite Product

Calculus Level 5

If \( \displaystyle z = \prod_{k=1}^{\infty} \left( 1 + \dfrac{i}{2k^2} \right) \), then what is the value of \((1-i)z + \text{Arg}(z)\)?

Give your answer to 3 decimal places.

Notation: \(\text{Arg}(z)\) represents the principal value of the angle of \(z\).

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