TS EAMCET · Maths · Complex Number
If is a complex cube root of unity, then
- A
- B
- C
- D
Answer & Solution
Correct Answer
(D)
Step-by-step Solution
Detailed explanation
Given that 1-ω+ω26+1-ω2+ω6 We know that 1+ω+ω2=0 & ω3=1 =-2ω6+-2ω26 =64ω6+64ω12 we know that ω3n=1. Required value=64+64=128.
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
- Let \(\overrightarrow{\mathbf{a}}\) be a unit vector, \(\overrightarrow{\mathbf{b}}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=\hat{\mathbf{i}}+3 \hat{\mathbf{k}}\). Then, maximum value of \([\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]\) isTS EAMCET 2008 Easy
- In a triangle ABC , if \(r_1 r_2+r_3=35, r_2 r_3+m_1=63\) and \(r_3 r_1+r r_2=45\), then \(2 s=\)TS EAMCET 2024 Medium
- If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-\mathrm{Px}^2+\mathrm{Q} x-\mathrm{R}=0\) and \((\alpha-2)^2,(\beta-2)^2\), \((\gamma-2)^2\) are the roots of the equation \(x^3-5 x^2+4 x=0\), then the possible least value of \(\mathrm{P}+\mathrm{Q}+\mathrm{R}\) isTS EAMCET 2025 Hard
- A and \({B}\) are two independent events. \({P}({A})=\frac{2}{5}, {P}({B})=\frac{1}{3}\). Match the following.


The correct answer is \( \begin{array}{llll} \mathbf{A} & \mathbf{B} & \mathbf{C} & \mathbf{D} \end{array} \)TS EAMCET 2022 Medium - Let \([A]_{3 \times 3}\) be a non-singular matrix such that \(A^{-1}=\frac{1}{3}\left(A^2-5 A+7 I\right)\).
Then \(17 A^8-85 A^7+119 A^6-51 A^5-19 A^4\) \(+95 A^3-133 A^2+58 A+I=\)TS EAMCET 2020 Medium - The volume (in cubic units) of the tetrahedron with edges \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) isTS EAMCET 2007 Easy
More PYQs from TS EAMCET
- The potential \(\phi(x, y)\) of an electrostatic field \(\mathbf{E}=a(\hat{y}+x \hat{\mathbf{j}})\) is [a is a constant and \(\hat{\mathbf{i}}\) and \(\hat{\mathbf{j}}\) are unit vectors along \(X\) and \(Y\) axes]TS EAMCET 2018 Easy
- TS EAMCET 2021 Medium
- Let \(e_1\) be the eccentricity of a hyperbola for which distance between its focii is 2 times the distance between its directrices and \(e_2\) be the eccentricity of another hyperbola for which the length of its transverse axis is twice the length of its the conjugate axis. Then \(e_1 e_2=\)TS EAMCET 2022 Medium
- If \(\int \frac{\sqrt{2} d x}{\cos x \sqrt{\sin 2 x}}=f(x)+c\), then \(f(x)=\)TS EAMCET 2019 Easy
- If the shortest distance between the lines \(\mathbf{r}=(3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})+t(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}})\) and \(\mathbf{r}=(\hat{\mathbf{i}}-7 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})+s(\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})\) is equivalent to projection of \(\mathbf{P}=-2 \hat{\mathbf{i}}+11 \hat{\mathbf{j}}\) on \(\mathbf{Q}\) then a possible vector \(\mathbf{Q}\) isTS EAMCET 2020 Medium
- If a plane \(\pi\) passes through the point \((-1,6,2)\) is perpendicular to the planes \(x+2 y+2 z-5=0\) and \(3 x+3 y+2 z-8=0\), then, the perpendicular distance from the point \((1,-1,1)\) to the plane \(\pi\) isTS EAMCET 2020 Easy