TS EAMCET · Maths · Complex Number
\(\frac{(1+i)^{2011}}{(1-i)^{2009}}\) is equal to
- A -1
- B 1
- C 2
- D -2
Answer & Solution
Correct Answer
(D) -2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \frac{(1+i)^{2011}}{(1-i)^{2009}}=\frac{(\sqrt{2})^{2011}\left(\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}\right)^{2011}}{(\sqrt{2})^{2009}\left(\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}}\right)^{2009}} \\ & =\frac{(\sqrt{2})^2\left(e^{\frac{i…
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