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# Complex question watch

1. A transformation, T, maps the point P from the z plane to Q in the w plane, defined below.

a) What is the locus of the point P, if P is mapped to Q which has locus .

b) Find the Cartesian equation of the circle, that the arc that represents the locus of P lies on.

c) Find the area bounded by the curve and the y axis.

Could someone just have a go and tell me what answer they got so that I can see if I'm right.
2. Anyone wanna have a go?
3. (Original post by Ano123)
A transformation, T, maps the point P from the z plane to Q in the w plane, defined below.

a) What is the locus of the point P, if P is mapped to Q which has locus .

b) Find the Cartesian equation of the circle, that the arc that represents the locus of P lies on.

c) Find the area bounded by the curve and the y axis.

Could someone just have a go and tell me what answer they got so that I can see if I'm right.
Is it the same as last night?
4. circle with centre ( -√ 3, -1 ) and radius 2
5. (Original post by TeeEm)
Is it the same as last night?
Yeah, just added the area bit on the end.
6. (Original post by the bear)
circle with centre ( -√ 3, -1 ) and radius 2
And the area?
7. (Original post by Ano123)
And the area?
I will have it by the end of the evening as I have a very long to do list on my desk
8. (Original post by Ano123)
And the area?
9. (Original post by the bear)
I got .
10. (Original post by Ano123)
I got .
11. If I am going to write a solution I might as well steal it
here is my version
Attached Images

12. (Original post by the bear)
How did you find the area?
13. (Original post by TeeEm)
If I am going to write a solution I might as well steal it
here is my version
Slightly different to how I did it. I defined the arc using parametric equations (I have them in my thread yesterday) and then integrated with respect to t.
14. (Original post by Ano123)
How did you find the area?
i counted the squares

i sketched the circle. i noticed that the sector of which the y axis formed a chord had a 60 degree angle.
i minused the triangles' area from the sector. job done

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