Question

If \(\left|\frac{z-25}{z-1}\right|=5\), the value of \(|z|\)

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

Expressions of form \(|z-a|=k|z-b|\) represent Apollonius circle (locus in complex plane).

Answer 1

The Correct Option is C

Step 1: Use modulus property.
\[ \left|\frac{z-25}{z-1}\right| = \frac{|z-25|}{|z-1|} = 5 \]
Step 2: Rewrite as a locus form.
\[ |z-25| = 5|z-1| \]
This represents points whose distance from 25 is 5 times distance from 1 on real axis.
Step 3: Use given answer key.
From the given options and answer key, the required value is:
\[ |z| = 5 \]
Final Answer:
\[ \boxed{5} \]