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Algebra Level pending

Define a complex number \(z\) which satisfied below expression:

\[z=\frac{1}{\sqrt2} +\frac{1}{\sqrt2}(\frac{1}{\sqrt2} +\frac{1}{\sqrt2}(\frac{1}{\sqrt2} +\frac{1}{\sqrt2}(...)^2)^2)^2\]

and the coefficient of the imagine part of \(z\) is positive.

Find argument of complex number \(z\) in degrees.

Clarification: You may assume that the argument is between \(0^\circ\) to \(360^\circ\).

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