AP EAMCET · Maths · Complex Number
If \(z_1=2+5 i, z_2=-1+4 i\) and \(z_3=1\), then \(\left|\frac{z_1-z_3}{z_3-z_2}\right|=\)
- A \(\sqrt{2}\)
- B \(2 \sqrt{2}\)
- C \(5 \sqrt{2}\)
- D \(4 \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{2}\)
Step-by-step Solution
Detailed explanation
Given: \(z_1=2+5 i, z_2=-1+4 i, z_3=i\) Now, \(\frac{z_1-z_3}{z_3-z_2}=\frac{2+5 i-i}{i-(-1+4 i)}=\frac{2+4 i}{1-3 i}\) \(=\frac{2(5 i-5)}{10}=\frac{10(i-1)}{10} \Rightarrow \frac{z_1-z_3}{z_3-z_2}=i-1\) Then, \(\left|\frac{z_1-z_3}{z_3-z_2}\right|=\sqrt{1+1}=2\)
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