AP EAMCET · Maths · Complex Number
If \(\alpha\) is the modulus of \(z_1=4+3 i\), then a point that does not lie in the region represented by \(\left|z-\overline{z_1}\right| \leq \alpha\) is
- A \(z_1-2 i\)
- B \(\mathrm{z}_1\)
- C \(2 z_1-7 i\)
- D \(3 \mathrm{z}_1-(10+8 \mathrm{i})\)
Answer & Solution
Correct Answer
(B) \(\mathrm{z}_1\)
Step-by-step Solution
Detailed explanation
Given \(z_1=4+3 i\) \(\Rightarrow\left|z_1\right|=\alpha=\sqrt{4^2+3^2}=5\) Now, \(|z-\overline{4+3 i}| \leq 5 \Rightarrow|z-(4-3 i)| \leq 5\) If we put \(\mathrm{z}=4+3 \mathrm{i}\) \(|4+3 i-4+3 i|=|6 i| \leq 5\) so \(z_1\) is not lies in \(\left|z-z_1\right| \leq \alpha\)
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