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AP EAMCET · Maths · Complex Number

If \(\mathrm{C}\) is a point on the straight line joining the points \(\mathrm{A}(-2+\mathrm{i})\) and \(\mathrm{B}(3-4 \mathrm{i})\) in the Argand plane and \(\frac{\mathrm{AC}}{\mathrm{CB}}=\frac{1}{2}\), then the argument of \(\mathrm{C}\) is

  1. A \(\tan ^{-1} 3\)
  2. B \(\tan ^{-1} 2-\pi\)
  3. C \(\tan ^{-1} 2\)
  4. D \(\pi-\tan ^{-1} 3\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\tan ^{-1} 2-\pi\)

Step-by-step Solution

Detailed explanation

Given the point \(\mathrm{A}(-2,1), \mathrm{B}(3,-4)\) \(\& \frac{\mathrm{AC}}{\mathrm{BC}}=\frac{1}{2}\) So, \(\mathrm{C} \equiv\left(\frac{1 \times 3-4}{3}, \frac{-4+2}{3}\right)=\left(\frac{-1}{3}, \frac{-2}{3}\right)\) Now, argument of…