A) 1
B) \[\pi \]
C) \[3\pi \]
D) 4
Correct Answer: D
Solution :
\[z=\frac{\pi }{4}{{(1+i)}^{4}}\left( \frac{1-\sqrt{\pi }i}{\sqrt{\pi }+i}+\frac{\sqrt{\pi }-i}{1+\sqrt{\pi }i} \right)\] \[=\frac{\pi }{4}{{(1+i)}^{4}}\left[ \frac{1+\pi +\pi +1}{(\sqrt{\pi }+i)(1+\sqrt{\pi }i)} \right]=\frac{\pi }{4}{{(1+i)}^{4}}\frac{2}{i}\] \[=\frac{\pi }{4}{{(2i)}^{2}}\frac{2}{i}=2\pi i\,\,\,\therefore \left( \frac{|z|}{amp(z)} \right)=\frac{2\pi }{\frac{\pi }{2}}=4\]
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