AP EAMCET · Maths · Complex Number
If \(\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2024}+\left(\frac{1+\cos \theta+i \sin \theta}{1-\cos \theta+i \sin \theta}\right)^{2025}=x+i y\), then the value of \(x+y\) at \(\theta=\frac{\pi}{2}\) is
- A 1
- B -1
- C 2
- D 2024
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\(\theta=\frac{\pi}{2}\): \(\left(\frac{\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}}{\sin \frac{\pi}{2}+i \cos \frac{\pi}{2}}\right)^{2024} = \left(\frac{0+i(1)}{1+i(0)}\right)^{2024} = i^{2024} = (i^4)^{506} = 1\) \(\theta=\frac{\pi}{2}\):…
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