TS EAMCET · Maths · Complex Number
\(n\) is a positive integer and not a multiple of 3 . If \(\omega\) is non real cube root of unity, then \(\omega^n+\omega^{2 n}\) is equal to
- A -1
- B 3
- C -3
- D 1
Answer & Solution
Correct Answer
(A) -1
Step-by-step Solution
Detailed explanation
If \(n\) is not a multiple of 3 , then \(n=3 K+1\) or \(n=3 K+2\) where \(K \in I\) Case (I) : When, \(n=3 K+1, K \in I\)…
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
- Seven balls are drawn simultaneously from bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is :TS EAMCET 2006 Medium
- If \(\left[\begin{array}{ccc}2 & 1 & 1 \\ 0 & 3 & -1 \\ 1 & -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 1 \\ 0\end{array}\right]\), then \(\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\)TS EAMCET 2020 Easy
- In a discrete data \(\frac{\text { lth }}{4}\) of the observations are equal to \(a\), another \(\frac{\text { th }}{4}\) of the observations are equal to \(-a\). Out of the remaining, half of them are equal to \(b\) and the rest are equal to \(-b\). If the variance of all the observations is \((a b)\), thenTS EAMCET 2020 Medium
- The equation of the circle passing through \((1,2)\) and the points of intersection of the circles \(x^2+y^2-8 x-6 y+21=0\) and \(x^2+y^2-2 x-15=0\), isTS EAMCET 2015 Medium
- If thenTS EAMCET 2020 Medium
- An integer is chosen from \(\{2 k /-9 \leq k \leq 10\}\). The probability that it is divisible by both 4 and 6 isTS EAMCET 2017 Easy
More PYQs from TS EAMCET
- The temperature of \(100 \mathrm{~g}\) of water is to be raised from \(24^{\circ} \mathrm{C}\) to \(90^{\circ} \mathrm{C}\) by adding steam at \(100^{\circ} \mathrm{C}\) to it. The mass of the steam required in this process is (latent heat of steam is \(540 \mathrm{cal} \mathrm{g}^{-1}\) )TS EAMCET 2023 Easy
- If the masses of three wires of same material are in the ratio of \(1: 2: 3\) and their lengths are in the ratio of \(3: 2: 1\), then electrical resistances of these wires are in the ratioTS EAMCET 2023 Easy
- A point \(P\) moves so that distance from \((0,2)\) to \(P\) is \(\frac{1}{\sqrt{2}}\) times the distance of \(P\) from \((-1,0)\). Then the locus of the point isTS EAMCET 2020 Easy
- Which one of the following is used as an acid flux in metallurgy?TS EAMCET 2004 Easy
- Two vessels separately contain two ideal gases and at the same temperature. The pressure of gas is three times the pressure of gas . Under these conditions, the density of gas is found to be two times the density of . The ratio of molecular weights of gas and i.e. isTS EAMCET 2020 Hard
- Electromagnetic radiation of intensity \(0.6 \mathrm{Wm}^{-2}\) is falling on a black surface. The radiation pressure on the surface isTS EAMCET 2023 Easy