AP EAMCET · Maths · Complex Number
\(\left(\frac{1+i}{1-i}\right)^4+\left(\frac{1-i}{1+i}\right)^4\) is equal to
- A \(0\)
- B \(1\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\begin{aligned}\left(\frac{1+i}{1-i}\right)^4 & +\left(\frac{1-i}{1+i}\right)^4 \\ & =\left\{\frac{(1+i)(1+i)}{(1-i)(1+i)}\right\}^4+\left\{\frac{(1-i)(1-i)}{(1+i)(1-i)}\right\}^4 \\ & =\left\{\frac{(1+i)^2}{1-i^2}\right\}^4+\left\{\frac{(1-i)^2}{1-i^2}\right\}^4 \\ &…
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