Is the Shaded Region Outside the Circle in the W Plane?

[trew]

Homework Statement

[/B]

Homework Equations

The Attempt at a Solution

I had no problems with part a and was able to form the equation of the circle and get its centre/radius.

It's part b that I'm stuck on.

My notes show that for Z < 3 I would shade inside the circle but the mark scheme for this question is showing the circle but the region shaded is OUTSIDE the circle.

Does this have something to do with the transformation into the W plane?

 

[BvU]

Hello Trew,

You can't write ${\bf z} < 3$ for a complex number ... it's $|{\bf z}| < 3$ as in the problem description.
The latter is inside the circle in the $\bf z$ plane -- as in your notes

But the exercise asks for the image (the complex 'range') of the function (transformation), so, as you suspect, in the $\bf w$ plane.

 

[trew]

Hello Trew,

You can't write ${\bf z} < 3$ for a complex number ... it's $|{\bf z}| < 3$ as in the problem description.
The latter is inside the circle in the $\bf z$ plane -- as in your notes

But the exercise asks for the image (the complex 'range') of the function (transformation), so, as you suspect, in the $\bf w$ plane.

Hey BvU,

Appreciate the response and help.

So is it a case of it being the opposite if it is transformed into the W-plane?

 

[BvU]

You say already found the circle in the W plane ? Check where a pont with $|{\bf z}| < 3$ ends up !
And double check with some points with $|{\bf z}| > 3$ !