Imaginary number challenge(2)

Algebra Level 5

\[\huge |(\sqrt[2-i]{1+i})^{3+i}| = \sqrt{a}e^{-\frac{\pi}{b}}\]

The above expression is in the simplest form , where \(a\) and \(b\) are positive integers.

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

Clarification: \(i=\sqrt{-1}\) , \(e\) is Euler's number and | . | denotes that absolute value function .

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

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