AP EAMCET · Maths · Complex Number
If \(z_1=(2,-1)\) and \(z_2=(6,3)\), then \(\operatorname{amp}\left(\frac{z_1-z_2}{z_1+z_2}\right)=\)
- A \(-\frac{3 \pi}{4}-\tan ^{-1}\left(\frac{1}{4}\right)\)
- B \(\frac{\pi}{4} \tan ^{-1}\left(\frac{1}{4}\right)\)
- C \(\frac{3 \pi}{4}+\tan ^{-1}\left(\frac{1}{4}\right)\)
- D \(\frac{\pi}{4}+\tan ^{-1}\left(\frac{1}{4}\right)\)
Answer & Solution
Correct Answer
(A) \(-\frac{3 \pi}{4}-\tan ^{-1}\left(\frac{1}{4}\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given } z_1=2-i, \quad z_2=6+3 i \\ & \operatorname{amp}\left(\frac{z_1-z_2}{z_1+z_2}\right)=\operatorname{amp}\left(\frac{-4-4 i}{8+2 i}\right) \\ & =\operatorname{amp}(-4-4 i)-\operatorname{amp}(8+2 i) \\ & =\left[\tan ^{-1}(1)-\pi\right]-\left[\tan…
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