AP EAMCET · Maths · Complex Number
If \(z\) is a complex number, then curves \(|z|=1\), \(|z-2|=1\) and \(|z-1|=0\) have a common point at
- A \((0,1)\)
- B \((2,0)\)
- C \((1,0)\)
- D \((0,2)\)
Answer & Solution
Correct Answer
(C) \((1,0)\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { } \because|z|=1,|z-2|=1,|z-1|=0 \\ & \because \quad|z|=1 \Rightarrow x^2+y^2=1...(i) \\ & |z-2|=1 \Rightarrow(x-2)^2+(y)^2=1 ...(ii) \\ & |z-1|=0 \Rightarrow(x-1)^2+y^2=0...(iii) \end{aligned} \] Solving Eqs. (i) and (ii), we get…
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