AP EAMCET · Maths · Complex Number
If \(z_1=10+6 i, z_2=4+6 i\) an \(z\) is any complex number such that the argument of \(\frac{\left(z-z_1\right)}{\left(z-z_2\right)}\) is \(\frac{\pi}{4}\), then
- A \(|z-7-9 i|=3 \sqrt{2}\)
- B \(|z-7-9 i|=2 \sqrt{2}\)
- C \(|z-3+9 i|=3 \sqrt{2}\)
- D \(|z+3-9 i|=2 \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(|z-7-9 i|=3 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(\operatorname{arg}\left(\frac{z-z_1}{z-z_2}\right)=\frac{\pi}{4}\) Locus of \(z\) lies on circle Angle subtended at centre \(=\frac{\pi}{2}\) Centre of circle is \((7+9 i)\) Radius \(=3 \sqrt{2}\) \(|z-(7+9 i)|=3 \sqrt{2}\)
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