# Face the Complexity

Algebra Level 5

We are all aware of the floor function but we don't have any concept on floor function of complex numbers. So, let's assume floor function of $$z$$ like this

$\large \lfloor z \rfloor = \lfloor \Re(z) \rfloor + i \lfloor \Im(z) \rfloor$

If you give some trials on $$\lfloor z \rfloor$$ you will see it is a point in the complex plane. For some particular complex numbers it will maps to a single point.

Find number of all distinct values of $$\lfloor z \rfloor$$ for every $$|z| \leq 8$$

Notations: $$\Re(z)$$ and $$\Im(z)$$ is the real part and complex part of $$z$$.

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