Complex? No.

Algebra Level 5

If \( { z }_{ 1 }={ e }^{ i\pi /4 }\\ { z }_{ 2 }={ 2e }^{ i\pi /6 }\\ { z }_{ 3 }=4\\ { z }_{ 4 }=2i\)

What is the absolute value of \({ z }_{ 1 }^{ 8 }-{ z }_{ 4 }^{ 4 }{ e }^{ \sec(i{ z }_{ 2 })\cosh({ z }_{ 2 })-i\sinh({ z }_{ 3 })csc(i{ z }_{ 3 }) }\)?

Credits to Engr. Ted

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