Given, \( z=\cos \frac{2 \pi}{2 n+1}+i \sin \frac{2 \pi}{2 n+1} \), \( n \) a positive integer...
Given, \( z=\cos \frac{2 \pi}{2 n+1}+i \sin \frac{2 \pi}{2 n+1} \), \( n \) a positive integer, find the equation whose roots are, \( \alpha=z+z^{3}+\ldots+z^{2 n-1} \) and \( \beta=z^{2} \) \( +z^{4}+\ldots+z^{2 n} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-07-03 | Let \( S=z \in C:|z-3| \leq 1 \) and \( z(4+3 i)+\bar{z}(4-3 i) \leq 24 \).
If \( \alpha+i \beta... |
| 2023-07-03 | The area of the triangle with vertices \( A(z), B(i z) \) and \( C(z+ \) \( i z) \) is :
(a) \( ... |
| 2023-07-03 | On the Argand plane \( z_{1}, z_{2} \) and \( z_{3} \) are respectively the vertices of an isosc... |
| 2023-07-03 | Let \( \mathrm{z} \) be those complex numbers which satisfy \( |z+5| \leq 4 \) and \( z(1+i)+\ba... |
| 2023-07-03 | Show that all roots of the equation \( a_{0} z^{n}+a_{1} z^{n-1}+\ldots+a_{n-1} z \) \( +a_{n}=n... |
| 2023-07-03 | If \( P \) is a point on the Aragand diagram. On the circle with \( O P \) as diameter two point... |
| 2023-07-03 | \( z_{1}, z_{2} \) and \( z_{3} \) are three non-zero complex numbers such that \( z_{1} \neq z_... |
| 2023-07-03 | If \( z_{1} \) and \( z_{2} \) are two complex number and if \( \arg \frac{z_{1}+z_{2}}{z_{1}-z_... |
| 2023-07-03 | Let \( A \equiv z_{1} ; B \equiv z_{2} ; C \equiv z_{3} \) are three complex numbers denoting th... |
| 2023-07-03 | Let \( z_{1}, z_{2}, z_{3} \) are three pair wise distinct complex numbers and \( t_{1}, t_{2}, ... |
| 2023-07-03 | Given, \( z=\cos \frac{2 \pi}{2 n+1}+i \sin \frac{2 \pi}{2 n+1} \), \( n \) a positive integer... |
| 2023-07-03 | The points \( A, B, C \) represent the complex numbers \( z_{1}, z_{2}, z_{3} \) respectively on... |
| 2023-07-03 | A particle starts to travel from a point \( P \) on the curve \( C_{1} \) : \( |z-3-4 i|=5 \), w... |
| 2023-07-03 | \( \omega_{1}, \omega_{2}, \ldots, \omega_{n} \) be complex numbers. A line \( L \) in the argan... |
| 2023-07-03 | If \( \omega \) is the imaginary cube root of unity, then find the number of pairs of integers \... |
| 2023-07-03 | If \( \mathrm{z} \in C \), then the locus of \( z \) on an Argand diagram is
\begin{tabular}{|l|... |
| 2023-07-03 | If \( \mathrm{z} \in C \), then the locus of \( z \) on an Argand diagram is
\begin{tabular}{|l|... |
| 2023-07-03 | Assume that \( A_{\mathrm{i}}(i=1,2, \ldots, n) \) are the vertices of a regular polygon inscrib... |
| 2023-07-03 | If \( z \) is a complex number and the minimum value of \( |z|+|z-1| \) \( +|2 z-3| \) is \( \la... |
| 2023-07-03 | If \( z_{1}, z_{2}, z_{3} \) be vertices of an isosceles \( \Delta \) right angled at \( z_{3} \... |
| 2023-07-03 | Let \( z_{1}, z_{2}, \ldots, z_{n} \) be in G.P with first term as unity such that \( z_{1}+z_{2... |
0