I have to graphically represent the following subset in the complex plane being z a complex number: A = 1 &lt; | z | &lt; 2 What I did previously was solve it like it was a regular inequality system in the real numbers, resulting in b &lt; − a + 4 and b &gt; − a + 1How can I solve this?

Question

I have to graphically represent the following subset in the complex plane being z a complex number:   A  =      1    &amp;lt;      |    z      |    &amp;lt;    2  What I did previously was solve it like it was a regular inequality system in the real numbers, resulting in   b  &amp;lt;  −  a  +  4 and   b  &amp;gt;  −  a  +  1How can I solve this?

Campasenabs · Accepted Answer

The geometric interpretation of this would be an open annulus centred at   0 with inner radius   1 and outer radius   2.To see this, observe that   |  z  | represents the Euclidean distance from   z to   0. The condition   1  &amp;lt;  |  z  | restricts   z to be outside of the unit disk, and similarly for   |  z  |  &amp;lt;  2.Hint:   |  z  | is the distance from   z to   0. So geometrically,   1  &amp;lt;  |  z  |  &amp;lt;  2 is the region inside and outside

cricafh · Accepted Answer

This would be the shaded region between the circles       x    2    +      y    2    =  4 and       x    2    +      y    2    =  1

I have to graphically represent the following subset in the complex plane being z a complex number:

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