# Argand diagram regionsWatch

#1
Hi,

I'm doing the following question:

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.
0
2 years ago
#2
(Original post by Sir_Malc)
Hi,

I'm doing the following question:

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 . An obvious one is , this satisfies . This is a point inside the circle .

Now where does this point map to? Well, , which is outside your -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.
1
#3
(Original post by Zacken)
Literally just choose a test point that satisfies . An obvious one is , this satisfies . This is a point inside the circle .

Now where does this point map to? Well, , which is outside your -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.
0
2 years ago
#4
(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.
0
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