TS EAMCET · Maths · Complex Number
\(\sum_{r=1}^{16}\left(\sin \frac{2 r \pi}{17}+i \cos \frac{2 r \pi}{17}\right)=\)
- A 1
- B -1
- C \(i\)
- D \(-i\)
Answer & Solution
Correct Answer
(D) \(-i\)
Step-by-step Solution
Detailed explanation
We have, \[ \sum_{r=1}^{16}\left(\sin \frac{2 r \pi}{17}+i \cos \frac{2 r \pi}{17}\right)=i \sum_{r=1}^{16}\left(\cos \frac{2 r \pi}{17}-i \sin \frac{2 r \pi}{17}\right) \]…
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 the vector \(\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\) and \(\mathbf{b}\) are collinear and \(|\mathbf{b}|=21\), then \(\mathbf{b}\) equal to:TS EAMCET 2005 Easy
- If the general solution of the differential equation \((y-x+1) d y-(y+x+2) d x=0\) is \(f(x, y, c)=0\), then the value of \(c\) such that \(f(1,1, c)=0\) isTS EAMCET 2020 Easy
- If \(A=\left[\begin{array}{cc}-1 & 0 \\ 0 & 2\end{array}\right]\), then \(A^3-A^2\) is equal toTS EAMCET 2005 Medium
- The mean and variance of a binomial variate \(X\) are \(\frac{16}{5}\) and \(\frac{48}{25}\) respectively. If \(P(X\gt1)=1-K\left(\frac{3}{5}\right)^7\), then \(5 K=\)TS EAMCET 2024 Hard
- The position vectors of the points and are respectively and The ratio in which the point having position vector divides the line segment joining and isTS EAMCET 2021 Easy
- If \(A_i(i=1,2,3, \ldots, n)\) are \(n\) independent events with \(P\left(A_i\right)=\frac{1}{1+i}\) for each \(i\), then the probability that none of \(A_i\) occurs isTS EAMCET 2010 Easy
More PYQs from TS EAMCET
- Identify the correct order of reactivity of the following haloarenes on treatment with \(\mathrm{NaOH} ?\)
TS EAMCET 2019 Easy - Let \(\mathrm{m}, \mathrm{n}, \mathrm{p}, \mathrm{q}\) be four positive integers. If \(\int_0^{2 \pi} \sin ^m x \cos ^n x d x=4 \int_0^{\pi / 2} \sin ^m x \cos ^n x d x\), \(\int_0^{2 \pi} \sin ^p x \cos ^n x d x=0, \int_0^\pi \sin ^p x \cos ^q x d x=0, \mathrm{a}=\mathrm{m}+\mathrm{n}+\mathrm{p}\) and \(\mathrm{b}=\mathrm{m}+\mathrm{n}+\mathrm{q}\), thenTS EAMCET 2025 Hard
- A motor-bike starts from rest, attains a velocity of \(10 \mathrm{~m} / \mathrm{s}\) with an acceleration of \(0.5 \mathrm{~m} / \mathrm{s}^2\), travels \(10 \mathrm{~km}\) with this uniform velocity and then comes to halt with a uniform deceleration of \(0.2 \mathrm{~m} / \mathrm{s}^2\). The total time of travel isTS EAMCET 2020 Easy
- The heat evolved for the rise of water when one end of the capillary tube of radius \(r\) is immersed vertically into water is (Assume surface tension \(=T\) and density of water to be p)TS EAMCET 2005 Hard
- \(x=\frac{1}{2}\left(\sqrt{3}+\frac{1}{\sqrt{3}}\right)\), then \(\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}\) is equal toTS EAMCET 2005 Medium
- Which of the below reactions produce carboxylic acids?
(a)
\(\frac{ MnO _2}{ CH _3 COCH _3}\)
(b)
(c)
(d)TS EAMCET 2019 Easy