If \( z=\frac{\pi}{4}(1+i)^{4}\left(\frac{1-\sqrt{\pi} i}{\sqrt{\pi...

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If \( z=\frac{\pi}{4}(1+i)^{4}\left(\frac{1-\sqrt{\pi} i}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi} i}\right) \), where \( i=\sqrt{-1} \),
P then \( \left(\frac{|z|}{\operatorname{amp}(z)}\right) \) equals to
(1) 1
(2) 2
(3) 3
(4) 4
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