Question: Plotting a graphs using Complex expressions

How do i plot both A & B on the same set of axes where

A={z:1<=|z+2i|<=2}; & B={z:1<=|Arg(z+2i)|<Pi/3}.

I'm struggling to plot A on it's own nevermind B!

restart; g:= x^2+(y+2)^2<=2; plots[implicitplot](g,x=-5..5,y=-5..5,y=-5..5,filled = true, scaling = constrained)

I'd have thought when |z+2i|=2 my circle should should go through the origin but with the above code it does not. Am i completely wrong here?

And how do i plot it with 1<= and >=2?

Any pointers would be very much appreciated.



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