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If $z=x+i y$ represents a point $P$ in the argand plane, then the area of the region represented by the inequality $2 < |z-(1+i)| < 3$ is
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Verified Answer
The correct answer is:
$5 \pi$
We have,
$$
\begin{aligned}
& z=x+i y \\
& \text { and } \quad 2 < |z-(1+i)| < 3 \\
& 2 < |(x-1)-(y-1) i| < 3 \\
& 4 < (x-1)^2+(y-1)^2 < 9 \\
&
\end{aligned}
$$
Area of region $=$ Area of largest circle
Area of smallest circle
$9 \pi-4 \pi=5 \pi$
$$
\begin{aligned}
& z=x+i y \\
& \text { and } \quad 2 < |z-(1+i)| < 3 \\
& 2 < |(x-1)-(y-1) i| < 3 \\
& 4 < (x-1)^2+(y-1)^2 < 9 \\
&
\end{aligned}
$$
Area of region $=$ Area of largest circle
Area of smallest circle
$9 \pi-4 \pi=5 \pi$
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