TS EAMCET · Maths · Complex Number
If \(\mathrm{i}=\sqrt{-1}\) then \(\operatorname{Arg}\left[\frac{(1+\mathrm{i})^{2025}}{(1-\mathrm{i})^{2022}}\right]=\)
- A \(\frac{-\pi}{4}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{3 \pi}{4}\)
- D \(\frac{-3 \pi}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{-\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\arg \left[\frac{(1+i)^{2025}}{(1-i)^{2022}}\right]\) \(\frac{(1+i)^{2025}}{(1-i)^{2022}}=\frac{(\sqrt{2})^{2025}\left(\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}\right)^{2025}}{(\sqrt{2})^{2022}\left(\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}}\right)^{2022}}\)…
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