Complex numbers revision

Algebra Level 4

Find the complex number \(z\) such that \(\left| z-2+2i \right| \le 1\) and \(z\) has the least absolute value.

The answer is of the form: \(\left( a-\frac { 1 }{ \sqrt { b } } \right) \left( c-i \right) \)

Find \(a+b+c\).

where \(b\) is not a perfect square, and \(i = \sqrt { -1 } \)

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