Complex Numbers And Quadratic Equations question 500

Question: If $ z=\frac{\pi }{4}{{( 1+i )}^{4}}( \frac{1-\sqrt{\pi }i}{\sqrt{\pi }+i}+\frac{\sqrt{\pi }-i}{1+\sqrt{\pi }i} ) $ , then find $ ( \frac{| z |}{Amp( z )} ) $ .

Solution:

Answer: 4.00