# 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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