# 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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