AP EAMCET · Maths · Complex Number
\((-i+\sqrt{3})^{300}+(-i-\sqrt{3})^{300}=\)
- A \(2^{300}\)
- B \(2^{301}\)
- C \(2^{100}\)
- D \(-2^{300}\)
Answer & Solution
Correct Answer
(B) \(2^{301}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} &(-i+\sqrt{3})^{300}+(-i-\sqrt{3})^{300}=(i-\sqrt{3})^{300} +(-i-\sqrt{3})^{300} \\ &= i^{300}(1+i \sqrt{3})^{300}+i^{300}(-1+i \sqrt{3})^{300} \\ &=\left(-2 w^2\right)^{300}+(2 w)^{300} \quad\{\text {where } w \text { is cube root of unity}\} \\ &=…
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