TS EAMCET · Maths · Complex Number
If \(\omega\) is a complex cube root of unity, then \(\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}\) is equal to
- A \(\frac{1}{\sqrt{2}}\)
- B \(\frac{1}{2}\)
- C \(1\)
- D \(\frac{\sqrt{3}}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Since, \(\omega\) is a cube root of unity.…
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
- The shortest distance between the skew lines \(\frac{x-2}{1}=\frac{y-3}{-2}=\frac{x+5}{1}\) and \(\frac{x-1}{-1}=\frac{y+2}{3}=\frac{z-4}{2}\) isTS EAMCET 2020 Easy
- \(\int \frac{d x}{7+5 \cos x}\) is equal toTS EAMCET 2002 Medium
- If \(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(x^4+x^2+1=0\) such that \(\alpha+\beta=-1, \gamma+\delta=1, \alpha^2=\beta\) and \(\gamma^2=-\delta\), then \(\alpha^{2023}+\beta^{2023}+\gamma^{2022}+\delta^{2022}=\)TS EAMCET 2023 Hard
- If \(\bar{a}=(x+2 y-3) \bar{i}+(2 x-y+3) \bar{j}\) and \(\bar{b}=(3 x-2 y) \bar{i}+(x-y+1) \bar{j}\) are two vectors such that \(\bar{a}=2 \bar{b}\), then \(y-5 x=\)TS EAMCET 2025 Medium
- If \(a\) and \(b\) respectively represent the leng ths of a side and a diagonal of a regular pentagon that is inscribed in a circle, then \(\frac{b}{a}=\)TS EAMCET 2019 Easy
- \(x\) and \(y\) are two positive integers such that \(2 x+3 y=50\). If \(x^2 y^3\) is maximum for \(x=\alpha\) and \(y=\beta\), then \(\frac{\alpha}{2}+\frac{\beta}{5}=\)TS EAMCET 2023 Easy
More PYQs from TS EAMCET
- In a well pressure at a point \(10 \mathrm{~m}\) below the surface of water is \(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)TS EAMCET 2023 Easy
- A compound having elements \(X\) and \(Y\) crystallises in a cubic structure, where \(X\) is at the corner position and \(Y\) is at the center of the cube. The correct formula of the compound isTS EAMCET 2018 Easy
- Let \(S_r=\{x, y, z) / x+y+z=11, x \geq r, y \geq r\), \(z \geq r, x, y, z, r\) are integers \(\}\) and \(n\left(S_r\right)\) represents the number of elements in \(S_r\). Then \(n\left(S_{2)}+n\left(S_3\right)+n\left(S_4\right)=\right.\)TS EAMCET 2020 Easy
- A simple pendulum consists of a small sphere of mass suspended by a thread of length . The sphere carries a positive charge . The pendulum is allowed to do small oscillations in a uniform electric field with direction vertically upwards. The time period of oscillation isTS EAMCET 2022 Easy
- The total number of spectral lines observed when electron returns from the shell until the shell in hydrogen atom isTS EAMCET 2022 Medium
- \(x\) grams of water is mixed in \(69 \mathrm{~g}\) of ethanol. Mole fraction of ethanol in the resultant solution is 0.6 . What is the value of \(x\) in grams?TS EAMCET 2004 Easy