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    Hi,

    I'm doing the following question:

    Name:  maths2.png
Views: 48
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    I can do part a. Where I get a circle centre (9/8, 0), radius 3/8

    I can sketch this fine, but I don't know how to plug in |z| < 3 in order to find the Region R.

    I shaded in the inside of the circle but apparently its the region outside it.

    Thanks,
    Malc.
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    (Original post by Sir_Malc)
    Hi,

    I'm doing the following question:

    Name:  maths2.png
Views: 48
Size:  105.6 KB

    I can do part a. Where I get a circle centre (9/8, 0), radius 3/8

    I can sketch this fine, but I don't know how to plug in |z| < 3 in order to find the Region R.

    I shaded in the inside of the circle but apparently its the region outside it.

    Thanks,
    Malc.
    Literally just choose a test point that satisfies |z| &lt; 3. An obvious one is z=i, this satisfies |z| = 1 &lt; 3. This is a point inside the circle |z| &lt;3.

    Now where does this point map to? Well, w = \frac{z}{z+i} = \frac{i}{2i} = \frac{1}{2}, which is outside your w-circle.

    You've just shown that a point inside the z circle gets mapped to a point outside the w circle. It'd be nice if you could mark these points on your sketch to help you visualise what's going on.
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    (Original post by Zacken)
    Literally just choose a test point that satisfies |z| &lt; 3. An obvious one is z=i, this satisfies |z| = 1 &lt; 3. This is a point inside the circle |z| &lt;3.

    Now where does this point map to? Well, w = \frac{z}{z+i} = \frac{i}{2i} = \frac{1}{2}, which is outside your w-circle.

    You've just shown that a point inside the z circle gets mapped to a point outside the w circle. It'd be nice if you could mark these points on your sketch to help you visualise what's going on.
    Thankyou.

    I tested a few other points and it works like you said.

    Many thanks.
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    (Original post by Sir_Malc)
    Thankyou.

    I tested a few other points and it works like you said.

    Many thanks.
    Cheers! You'll only need to test one point in the actual exam.
 
 
 
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