Q47 / 160 · AP EAMCET 2023 (17 May Shift 2) · Mathematics

If $z_1=2+5 i, z_2=-1+4 i$ and $z_3=1$, then $\left|\frac{z_1-z_3}{z_3-z_2}\right|=$

  • Correct answer
    A
    $\sqrt{2}$
  • B
    $2 \sqrt{2}$
  • C
    $5 \sqrt{2}$
  • D
    $4 \sqrt{2}$

Solution

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, $\left|\frac{z_1-z_3}{z_3-z_2}\right|=\sqrt{1+1}=2$

Hence, the correct answer is option: 'A'.

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