# Complex on Complex

Algebra Level 5

Suppose that:

$\large \left(\sqrt{2} + i\dfrac{\sqrt{2}}{3}\right)^{(1+i)} = \alpha + i \beta$

where, $$\alpha$$ and $$\beta$$ are real numbers and $$i^2 = - 1$$. Find $$\lfloor 1000\alpha \rfloor + \lfloor 1000\beta \rfloor$$, where $$\lfloor x \rfloor$$ is the greatest integer function.

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