TS EAMCET · Maths · Complex Number
The number of points \(z\) on the Argand plane which satisfy the conditions \(\operatorname{Re}\left(\frac{z-2}{z-4 i}\right)=0\) and \(\lim \left(\frac{z-2}{z-4 i}\right)=1\) simultaneously is
- A 0
- B 1
- C 2
- D infinitely many
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
Given \(\operatorname{Re}\left(\frac{z-2}{z-4 i}\right)=0\) and \(m\left(\frac{z-2}{z-4 i}\right)=1\) \(\Rightarrow \quad \frac{z-2}{z-4 i}=i \Rightarrow z-2=i(z-4 i)\) \(\Rightarrow \quad z-2=i z+4 \Rightarrow z(1-i)=6\)…
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