A New Meaning to Complex Roots

Algebra Level 4

If real number \(k\ne 1\) is chosen so that \(\sqrt[1-i]{k}\) is real, then find the smallest possible positive value of \(\lfloor\sqrt[1-i]{k}\rfloor\).

\(\text{Details and Assumptions}\)

\(k\) is being taken to the \((1-i)\)th root.

You may use a scientific calculator.

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