[Charries]

Here's the question :

Question 10.



I get the first bit - essentially, make z subject, take 4, take mod, then equal to w, and you get |w| = |w-4|, so it's the line u=2. What I don't get is the second bit, where you are supposed the "hence" suss out the the interior area of the circle means that the shaded region is to the right of the line u=2. If I try to preserve the inequality from the question, I get |w| < |w-4|, but I'm not sure how to interpret it? The strict locus would be u=2, and if I think about the RHS of the inequality, I think the shaded region is to the right, but if I think about the LHS of the inequality, I think that the shaded region should be to the left?

Could someone please explain how I should go about this?

[mathz]

pick a point inside the circle. appl the transformation. what side of the line is it?..

[Charries]

Yes thought about that, but is there an easier way apart from substituting u+iv, multiplying by conjugate, equating real or imaginary parts, as this seems a bit long winded and not "hence", more otherwise?

[mathz]

your circle is (x-4)^2+y^2=16 ; 1+0i is inside that.

not too much work applying T to that.

[Charries]

Thanks.