If \( |\mathrm{z}|=1 \) and \( \mathrm{z}-1=\mathrm{ik}(\mathrm{z}+1) \), then find range of \( ...
If \( |\mathrm{z}|=1 \) and \( \mathrm{z}-1=\mathrm{ik}(\mathrm{z}+1) \), then find range of \( \mathrm{k} \) ?
(a) \( (-\infty, \infty) \)
(b) \( (-\infty, 0] \)
(c) \( [0, \infty) \)
(d) \( \{0\} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-07-03 | If \( \omega \) is an imaginary \( x^{n} \) root of unitythen \( \sum_{r=1}^{n}(a r+b) \omega^{r... |
| 2023-07-03 | If \( \alpha \) is the \( n^{\text {th }} \) root of unity, then \( 1+2 \alpha+3 \alpha^{2}+\ldo... |
| 2023-07-03 | The polynomial \( x^{6}+4 x^{5}+3 x^{4}+2 x^{3}+x+1 \) is divisible by
(a) \( x+\omega \)
(b) \(... |
| 2023-07-03 | Given \( \mathrm{f}(\mathrm{z})= \) the real part of a complex number \( \mathrm{z} \). For exam... |
| 2023-07-03 | If \( x=9^{1 / 3} 9^{1 / 9} 9^{1 / 27} \ldots \ldots \infty, y=4^{1 / 3} 4-1 / 94^{1 / 27} \ldot... |
| 2023-07-03 | If \( |z+1|+|z-3|=6 \) and \( |z|=|z-2| \), then find \( z \) ?
(a) \( 1 \pm \sqrt{5} i \)
(b) \... |
| 2023-07-03 | If \( z_{1}, z_{2}, z_{3} \) are three complex numbers and \( A=\left|\begin{array}{ccc}\arg z_{... |
| 2023-07-03 | Find the area bounded by the curves \( \operatorname{Arg} \mathrm{z}=\pi / 3 \), \( \operatornam... |
| 2023-07-03 | If \( x^{6}=(4-3 i)^{5} \), then the product of all of its roots \( \left(\right. \) where \( \l... |
| 2023-07-03 | A root of unity is a complex number that is a solution to the equation \( z^{n}=1 \) for some po... |
| 2023-07-03 | If \( |\mathrm{z}|=1 \) and \( \mathrm{z}-1=\mathrm{ik}(\mathrm{z}+1) \), then find range of \( ... |
| 2023-07-03 | Find the sum of the series. \( \cos \theta+\cos 2 \theta+\cos 3 \theta+\ldots+\cos n \theta \) f... |
| 2023-07-03 | The least positive integer \( n \) for which \( \left(\frac{1+i}{1-i}\right)^{n}=\frac{2}{\pi} \... |
| 2023-07-03 | Let \( z_{1} \neq z_{2} \) are two points in the argand plane. If \( a\left|z_{1}\right|=b\left|... |
| 2023-07-03 | If \( Z_{r} ; r=1,2,3, \ldots, 50 \) are the roots of the equation \( \sum_{r=0}^{50}(Z)^{r}=0 \... |
| 2023-07-03 | Let \( z_{1} \neq z_{2} \) are two points in the argand plane. If \( a\left|z_{1}\right|=b\left|... |
| 2023-07-03 | If \( x^{2}-x+1=0, \sum_{n=1}^{5}\left(x^{n}+\frac{1}{x^{n}}\right)^{2} \) equal
(a) 8
(b) 10
(c... |
| 2023-07-03 | If \( \alpha=\cos \left(\frac{8 \pi}{11}\right)+i \sin \left(\frac{8 \pi}{11}\right) \) then \( ... |
| 2023-07-03 | Let \( A\left(z_{1}\right), A_{2}\left(\bar{z}_{1}\right) \) are the adjacent vertices of a regu... |
| 2023-07-03 | If \( x_{n}=\cos \frac{\pi}{2^{n}}+i \sin \frac{\pi}{2^{n}} \), then \( x_{1} x_{2} x_{3} \ldots... |
| 2023-07-03 | The number of complex numbers satisfying \( |z+2|+|z-2| \) \( =8 \) and \( |z-1|+|z+1|=2 \) is
(... |
0