TS EAMCET · Maths · Complex Number
If \(i=\sqrt{-1}\), then \((1+i)^{10}+(1-i)^{10}=\)
- A \(-64\)
- B \(-64\)
- C \(-64\)
- D \(-64i\)
Answer & Solution
Correct Answer
(C) \(-64\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (1+i)^{10}+(1-i)^{10} \\ = & 2^5\left(\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}\right)^{10}+2^5\left(\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}}\right)^{10} \\ = & 2^5\left[\left(e^{i \pi / 4}\right)^{10}+\left(e^{-i \pi / 4}\right)^{10}\right]\end{aligned}\)…
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