if |z|=3 is a circle, how do you know if the region outside the circle is

|z|<3

Many thanks

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- Nov 26th 2011, 09:03 AMminicooper58complex inequalities
if |z|=3 is a circle, how do you know if the region outside the circle is

|z|<3

Many thanks - Nov 26th 2011, 09:12 AMPlatoRe: complex inequalities
- Nov 26th 2011, 09:27 AMminicooper58Re: complex inequalities
Hi , the question and answer is in the attachments . sorry i didn't fully explain the transformation part . I don't understand how the region is outside the circle for (b) .

Many thanks - Nov 26th 2011, 01:16 PMHallsofIvyRe: complex inequalities
That's not at all the question you originally asked! The set |z|< 3 is the

**inside**of the circle given by |z|= 3. But the function maps the circle |z|= 3, with center at 0 and radius 3, into the circle with center at and radius . It also clearly maps 0 to 0. 0 is inside |z|< 3 but**outside**the circle with center and radius . Therefore, the interior of the first circle is mapped to the exterior of the second circle.