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# Further Complex Numbers - Transformations watch

1. Could someone walk me through part b? and check my answer/method to part a?

The transformation T from the z-plane, where , to the w-plane, where , is given by

The transformation T maps the points on the line l with equation y=x in the z-plane to a circle C in the w-plane

a) Show that:

where a, b and c are real constants to be found.
Spoiler:
Show
As given,
Therefore we can let
Sub into , simplify, then multiply by the complex conjugate of the denominator.

b) Hence show that the circle C has equation

where k is a constant to be found.

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I don't know where to start.. yet (part b). I don't see it.

Much appreciated.
2. (Original post by edothero)

I don't know where to start.. yet (part b). I don't see it.

Much appreciated.
Agree with part a).

Part b) w=u+iv

So separate your w into real and imaginary parts (for your u and v) and sub into LHS of given equation.

I get k=
Spoiler:
Show

5
or -5
3. (Original post by ghostwalker)
Agree with part a).

Part b) w=u+iv

So separate your w into real and imaginary parts (for your u and v) and sub into LHS of given equation.

I get k=
Spoiler:
Show

5
or -5
I see, the value of k checks out for me also.
Though can the answer realistically be -5? as we are dealing with the radius?

4. (Original post by edothero)
I see, the value of k checks out for me also.
Though can the answer realistically be -5? as we are dealing with the radius?
Fair point. 5 it is.

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