7. (a) Shade the region in the complex plane defined by \begin{equation*} \{ z \in \mathbb{C} : |z + 2 + i| \le 1 \} \end{equation*} (b) Shade the region in the complex plane defined by \begin{equation*} \left\{ z \in \mathbb{C} : \left| \frac{z + 2 + i}{z - 2 - 5i} \right| \le 1 \right\} \end{equation*}
Added by Oscar C.
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Step 1
First, let's rewrite the inequality in terms of the distance between z and -2 - i: |z + 2 + i| ≤ 1 |z - (-2 - i)| ≤ 1 This means that the distance between z and -2 - i is less than or equal to 1. In other words, z lies within or on the circle centered at -2 Show more…
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