# An immediately inspiration

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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