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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