Argand diagram regions Watch

Sir_Malc
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Hi,

I'm doing the following question:

Name:  maths2.png
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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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Zacken
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(Original post by Sir_Malc)
Hi,

I'm doing the following question:

Name:  maths2.png
Views: 65
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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Sir_Malc
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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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Zacken
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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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