Complex question

OP

Anyone wanna have a go?

Reply 2

TeeEm

19

Original post by Ano123

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

\displaystyle w = \frac{2-iz}{z}, z \in \mathbb{C}, z\neq 0

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

arg(w)=\frac{ \pi }{3}

.

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?

Reply 3

circle with centre ( -√ 3, -1 ) and radius 2

Reply 4

OP

Original post by TeeEm

Is it the same as last night?

Yeah, just added the area bit on the end.

Reply 5

OP

Original post by the bear

circle with centre ( -√ 3, -1 ) and radius 2

And the area?

Reply 6

Original post by Ano123

And the area?

say please

Reply 7

TeeEm

19

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

Reply 8

OP

Original post by the bear

say please

I got

2\pi/3 -\sqrt3

.

Reply 9

Original post by Ano123

I got

4\pi/6 -\sqrt3

.

4\pi/6 -\sqrt3

Reply 10

TeeEm

19

If I am going to write a solution I might as well steal it
here is my version

OP

Original post by the bear

4\pi/6 -\sqrt3

How did you find the area?

Reply 12

OP

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.

Reply 13