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Complex Numbers Question~!

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q10 b ii) P33 S12

It's only one mark, but I just can't work it out :( Help anybody?

10
(b) (i) On a sketch of an Argand diagram, shade the region whose points represent complex
numbers satisfying the inequalities |z − 2 + 2i| ≤ 2,
arg z ≤ −1/4π and Re z ≥1, where Re z denotes the real part of z.
(ii) Calculate the greatest possible value of Re z for points lying in the shaded region

I can draw the argand diagram easily but how are we supposed to work out the last part?
 
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