(a) Let \( \mathrm{z}=\cos \theta+\mathrm{i} \sin \theta \). Then t...
(a) Let \( \mathrm{z}=\cos \theta+\mathrm{i} \sin \theta \). Then the value of \( \sum_{\mathrm{m}=1}^{15} \operatorname{Im}\left(\mathrm{z}^{2 \mathrm{~m}-1}\right) \) at \( \theta=2^{\circ} \) is
\( \mathrm{P} \)
W
(A) \( \frac{1}{\sin 2^{\circ}} \)
(B) \( \frac{1}{3 \sin 2^{\circ}} \)
(C) \( \frac{1}{2 \sin 2^{\circ}} \)
(D) \( \frac{1}{4 \sin 2^{\circ}} \)
π² PW App Link - https://bit.ly/YTAI_PWAP
π PW Website - https://www.pw.live/
Other Videos By PW Solutions
| 2023-02-25 | Let \( a, b, x \) and \( y \) be real numbers such that \( a-b=1 \)... |
| 2023-02-25 | Let \( \mathrm{s}, \mathrm{t}, \mathrm{r} \) be non-zero complex nu... |
| 2023-02-25 | Statement 1: The value of \( { }^{100} \mathrm{C}_{95}+{ }^{101} \m... |
| 2023-02-25 | For a non-zero complex number z, let \( \arg (\mathrm{z}) \) denote... |
| 2023-02-25 | Let \( \mathrm{w}=\frac{\sqrt{3}+\mathrm{i}}{2} \) and \( \mathrm{P... |
| 2023-02-25 | If \( 3^{1} \cdot{ }^{20} \mathrm{C}_{0}+\frac{3^{2}}{2} \cdot{ }^{... |
| 2023-02-25 | Let \( S=S_{1} \cap S_{2} \cap S_{3} \), where
P
\( S_{1}=\{z \in C... |
| 2023-02-25 | Let \( \mathrm{C}_{1} \) and \( \mathrm{C}_{2} \) are concentric ci... |
| 2023-02-25 | Let \( a, b \in R \) and \( a^{2}+b^{2} \neq 0 \). Suppose \( S=\le... |
| 2023-02-25 | Let \( z_{\mathrm{k}}=\cos \left(\frac{2 \mathrm{k} \pi}{10}\right)... |
| 2023-02-25 | (a) Let \( \mathrm{z}=\cos \theta+\mathrm{i} \sin \theta \). Then t... |
| 2023-02-25 | Evaluate: \( \sum_{p=1}^{32}(3 p+2)\left(\sum_{q=1}^{10}\left(\sin ... |
| 2023-02-25 | Match the equation in z, in Column-I with the corresponding values ... |
| 2023-02-25 | A particle starts to travel from a point \( \mathrm{P} \) on the cu... |
| 2023-02-25 | Let tangents at \( \mathrm{A}\left(\mathrm{z}_{1}\right) \) and \( ... |
| 2023-02-25 | Let \( z_{1}, z_{2}, z_{3} \) be non-zero complex numbers satisfyin... |
| 2023-02-25 | Let \( \bar{b} z+b \bar{z}=c \), (where \( b \) is a non-zero compl... |
| 2023-02-25 | If the vertices of triangle \( \mathrm{ABC} \) in argand plane are ... |
| 2023-02-25 | Equation of a straight line on the complex plane passing through a ... |
| 2023-02-25 | Let \( \mathrm{A}, \mathrm{B}, \mathrm{C} \) be three sets of compl... |
| 2023-02-25 | Let \( \mathrm{ABC} \) be a triangle such that \( \angle \mathrm{AC... |
1