TS EAMCET · Maths · Complex Number
Assertion (A) If the arguments of \(\bar{z}_1\) and \(z_2\) are \(\frac{\pi}{5}\) and \(\frac{\pi}{3}\) respectively, then \(\arg \left(z_1 z_2\right)\) is \(\frac{2 \pi}{15}\). Reason (R) For any complex number \(z\), \(\arg \bar{z}=\frac{\pi}{2}+\arg z\) The correct option among the following is
- A (A) is true, \((\mathrm{R})\) is true and \((\mathrm{R})\) is the correct explanation for \((A)\)
- B (A) is true, \((\mathrm{R})\) is true but \((\mathrm{R})\) is not the correct explanation for \((A)\)
- C \((A)\) is true but \((R)\) is false
- D \((A)\) is false but \((R)\) is true
Answer & Solution
Correct Answer
(C) \((A)\) is true but \((R)\) is false
Step-by-step Solution
Detailed explanation
We have, \(\arg \left(\bar{z}_1\right)=\frac{\pi}{5}, \arg \left(z_2\right)=\frac{\pi}{3}\) \(\therefore \quad \arg \left(z_1 z_2\right)=\arg \left(z_2\right)-\arg \left(\bar{z}_1\right)=\frac{\pi}{3}-\frac{\pi}{5}=\frac{2 \pi}{15}\) Also, \(\arg (\bar{z})=-\arg (z)\). (A) is…
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