# Quirky complex

Algebra Level 3

If $Z=\dfrac {\pi}{4}(1+\iota)^{4}\left (\dfrac {1-\sqrt {\pi}\iota}{\sqrt {\pi}+\iota}+\dfrac{\sqrt {\pi }-\iota}{1+\sqrt {\pi}\iota}\right)$Then find the value of $$\left (\dfrac {|Z|}{\text {amp} (Z)}\right)$$ .

Note:- $$\iota=\sqrt {-1}$$ ,$$\text {amp}$$ is the amplitude of the complex number.

×