AP EAMCET · Maths · Complex Number
If \(\left|\frac{z-25}{z-1}\right|=5\), then \(|z|=\)
- A 5
- B 3
- C 4
- D 10
Answer & Solution
Correct Answer
(A) 5
Step-by-step Solution
Detailed explanation
\(\left|\frac{z-25}{z-1}\right|=5\) Let \(\quad z=x+i y\) \[ \begin{array}{r} \left|\frac{x+i y-25}{x+i y-1}\right|=5 \\ \frac{|(x-25)+i y|}{|(x-1)+i y|}=5 \\ \frac{\sqrt{(x-25)^2+y^2}}{\sqrt{(x-1)^2+y^2}}=5 \end{array} \] Squaring on both sides,…
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