AP EAMCET · Maths · Complex Number
\(\operatorname{Arg}\left(\frac{4+2 i}{1-2 i}+\frac{3+4 i}{2+3 i}\right)\) lies in the interval
- A \(\left(\frac{\pi}{4}, \frac{\pi}{2}\right)\)
- B \(\left(-\pi, \frac{-\pi}{2}\right)\)
- C \(\left(\frac{-\pi}{2}, 0\right)\)
- D \(\left(0, \frac{\pi}{4}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{\pi}{4}, \frac{\pi}{2}\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {}\left(\frac{4+2 i}{1-2 i}+\frac{3+4 i}{2+3 i}\right) \\ & =\frac{(4+2 i)(2+3 i)+(3+4 i)(1-2 i)}{(1-2 i)(2+3 i)} \\ & =\frac{(2+16 i)+(11-2 i)}{(8-i)}=\frac{(13+14 i)}{(8-i)} \\ & =\frac{90+109 i}{64+1}=\frac{90}{65}+\frac{109}{65} i \\ & \arg…
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