{$i+\bar z:1<|z|<4, z \in \mathbb{C}$}. If I want to shade this region in Argand plane, is it from z=i+4 to z=i-4?
How can I justify this answer?
2026-05-14 07:37:42.1778744262
Graph on argand plane
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The region defined by $1< |z| < 4$ is the open annulus. Conjugating the annulus (i.e., $\bar{z}$ flips the annulus across the horizontal axis, which in this case has no effect. Then, adding $i$ translates the annulus.