AP EAMCET · Maths · Complex Number
If \(n\) is a positive integer, then \((1+i \sqrt{3})^n+(1-i \sqrt{3})^n\) is equal to
- A \(2^{n-1} \cos \frac{n \pi}{3}\)
- B \(2^n \cos \frac{n \pi}{3}\)
- C \(2^{n+1} \cos \frac{n \pi}{3}\)
- D \(2^{2 n} \cos \frac{n \pi}{3}\)
Answer & Solution
Correct Answer
(C) \(2^{n+1} \cos \frac{n \pi}{3}\)
Step-by-step Solution
Detailed explanation
We have,…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If and are two vectors such that and and are perpendicular, where is a positive scalar, thenAP EAMCET 2021 Easy
- \(\int \frac{\sin (x-a)}{\sin (x-b)} d x=A x+B \log |\sin (x-b)|+C \Rightarrow(A, B)=\)AP EAMCET 2017 Hard
- For which value of ' \(k\) ', the roots of equation \(2 x^2+5 x+k=0\) are rational?AP EAMCET 2020 Medium
- If \(y=\sin ^{-1}\left[x \sqrt{1-x}-\sqrt{x} \cdot \sqrt{1-x^2}\right]\) and \(0 < x < 1\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2021 Hard
- The equation of bisectors of the angle between the lines given by \(3 x^2+5 x y+4 y^2=0\) isAP EAMCET 2022 Easy
- The equation of a line which makes an angle of \(45^{\circ}\) with each of the pair of lines \(x y-x-y+1=0\) isAP EAMCET 2024 Easy
More PYQs from AP EAMCET
- What sized ring is formed when two carboxylic acids form a dimeric structure through intermolecular hydrogen bonding? (consider hydrogen bond as a bond)AP EAMCET 2020 Hard
- A bus is moving with a velocity of \(5 \mathrm{~ms}^{-1}\) towards a huge wall. The driver sounds horn of frequency \(165 \mathrm{~Hz}\). If the speed of sound in air is \(335 \mathrm{~ms}^{-1}\), the number of beats heard per second by the passengers in the bus will beAP EAMCET 2017 Medium
- The general solution of \(\frac{d y}{d x}=\cos ^2(x-y-1)\) is given by \(\mathrm{x}=\)AP EAMCET 2023 Medium
- If \(f(x)= \begin{cases}\frac{\cos a x-\cos b x}{x^2}, & x \neq 0 \\ \frac{1}{2}\left(a^2-b^2\right) & , x=0\end{cases}\)
where \(a, b\) are real and district constants, thenAP EAMCET 2017 Medium - \(\mathrm{CH}_3 \mathrm{COOH} \stackrel{\mathrm{LiAlH}_4}{\longrightarrow} A\)
\(\mathrm{A}+\mathrm{CH}_3 \mathrm{COOH} \stackrel{\mathrm{H}_3 \mathrm{O}^{+}}{\longrightarrow} \mathrm{B}+\mathrm{H}_2 \mathrm{O}\)
In the above reactions ' \(A\) ' and ' \(B\) ' respectively areAP EAMCET 2007 Hard - The value of \(\cot 70^{\circ}+4 \cos 70^{\circ}\) isAP EAMCET 2017 Medium