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    (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 ≤ −1/4pi 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 (circle with center 2,-2 and then draw the other two lines) easily but how are we supposed to work out the last part?

    Are we supposed to use spiral enlargement?
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    I think it just wants you to draw out the (pie slice shaped, I think) region and find the real coordinate of the right most corner.
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    The circle is bisected by the line y = -x ...you need to find the point where this diameter has its largest x value
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    (Original post by claptraptheninja)
    (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 ≤ −1/4pi 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 (circle with center 2,-2 and then draw the other two lines) easily but how are we supposed to work out the last part?

    Are we supposed to use spiral enlargement?
    For calculating ii) With notation of z=x+iy
    You have to solve the equation of
    |z-(2-2i)|^2\leq 4 for Re(z)=x
    (Re(z)-2)^2+(Im(z)+2)^2\leq 4
    From this
    Re(z)\leq\sqrt{4-(Im(z))^2}+2
    For maximum Im(z)=y=0
    So you will get the maximum value of Re(z)
    You can read down it from your sketch, too
 
 
 
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