AP EAMCET · Maths · Complex Number
Geometrically, the set \(\{z \in \mathbf{C}:|z-2-2 i| \leq 1\}\) represents
- A a closed circular disc with center at \((-2,-2)\) and with radius 1
- B a closed circular disc with center at \((2,2)\) and with radius 1
- C a closed circular disc with center at \((1,1)\) and with radius 0.5
- D a closed circular disc with center at \((-1,-1)\) and with radius 0.5
Answer & Solution
Correct Answer
(B) a closed circular disc with center at \((2,2)\) and with radius 1
Step-by-step Solution
Detailed explanation
Given inequality is \(|z-2-2 i| \leq 1\) Let \(z=x+i y\), then we get \(\begin{aligned} & & \sqrt{(x-2)^2+(y-2)^2} & \leq 1 \\ \Rightarrow & & (x-2)^2+(y-2)^2 & \leq 1 \end{aligned}\) The above inequality represents a closed circular disc with center at \((2,2)\) and with radius…
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