Imaginary number challenge(2)

Algebra Level 5

\[\large \left|\left(\sqrt[2-i]{1+i}\right)^{3+i}\right| = \sqrt a e^{-\pi/b}\]

The expression above holds true for positive integers \(a\) and \(b\), where \(a\) is square free.

Find the value of \(63a^{3}b\).

Notations:

Hint: Euler's Formula is the core of this problem.

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