AP EAMCET · Maths · Complex Number
If \(n\) is an integer which leaves remainder one when divided by three, then \((1+\sqrt{3} i)^n+(1-\sqrt{3} i)^n\) equals
- A \(-2^{n+1}\)
- B \(2^{n+1}\)
- C \(-(-2)^n\)
- D \(-2^n\)
Answer & Solution
Correct Answer
(C) \(-(-2)^n\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Now, }(1+\sqrt{3} i)^n+(1-\sqrt{3} i)^n \\ &= {\left[2\left(\frac{1+\sqrt{3} i}{2}\right)\right]^n+\left[2\left(\frac{1-\sqrt{3} i}{2}\right)\right]^n } \\ &=\left(-2 \omega^2\right)^n+(-2 \omega)^n \\ &=(-2)^n\left[\left(\omega^2\right)^{3…
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