If \( x=9^{1 / 3} \cdot 9^{1 / 9} \cdot 9^{1 / 27} \ldots \infty, y=4^{1 / 3} \cdot 4^{-1 / 9} \...
If \( x=9^{1 / 3} \cdot 9^{1 / 9} \cdot 9^{1 / 27} \ldots \infty, y=4^{1 / 3} \cdot 4^{-1 / 9} \cdot 4^{1 / 27} \ldots \infty \) and \( z=\sum_{r=1}^{\infty}(1+i)^{-r} \), where \( i=\sqrt{-1} \), then \( \arg (x+y z) \) is equal to
(a) 0
(b) \( -\tan ^{-1}\left(\frac{\sqrt{2}}{3}\right) \)
(c) \( -\tan ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)
(d) \( \pi-\tan ^{-1}\left(\frac{\sqrt{2}}{3}\right) \)
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