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If z = (pi/4)*(1 + i)⁴ * [ (1 - sqrt(pi)*i)/(sqrt(pi) + i) + (sqrt(pi) - i)/(1 + sqrt(pi)*i) ], then the value of |z| / amp(z) is:

1. 1
2. pi
3. 3*pi
4. 4

Correct answer: 4

Solution

The expression simplifies to z = 2*pi*i, so |z| = 2*pi and amp(z) = pi/2, giving the ratio 4.

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