Complex-th Root

Algebra Level 5

\[ \LARGE \sqrt[1+i]{1+i}\] If the absolute value of the above expression can be written in the simplest form of \[\LARGE \sqrt[a]{b}e^{\pi/c}\] where \(a, b, c\) are integers. Find the value of \(\large abc - (a + b + c)\).

Note that \(i\) denote the imaginary number and \(e\) is Euler's number.

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