The value of \( \sum_{n=0}^{50} i^{(2 n+1) !}( \) where, \( i=\sqrt{-1}) \) is
(a) \( i \)
(b) \...
The value of \( \sum_{n=0}^{50} i^{(2 n+1) !}( \) where, \( i=\sqrt{-1}) \) is
(a) \( i \)
(b) \( 47-i \)
(c) \( 48+i \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
2022-10-27 | If \( \left|z_{1}\right|=\left|z_{2}\right| \) and \( \operatorname{amp}\left(z_{1}\right)+\oper... |
2022-10-27 | The principal value of \( \arg (z) \), where \( z=\left(1+\cos \frac{8 \pi}{5}\right)+i \sin \fr... |
2022-10-27 | The amplitude of \( e^{e^{-\theta}} \), where \( \theta \in R \) and \( i=\sqrt{-1} \) is
(a) \(... |
2022-10-27 | If \( z=i^{i^{i}} \), where \( i=\sqrt{-1} \), then \( |z| \) is equal to
(a) 1
(b) \( e^{-\pi /... |
2022-10-27 | If \( \left|z_{1}\right|=2,\left|z_{2}\right|=3,\left|z_{3}\right|=4 \) and \( \left|z_{1}+z_{2}... |
2022-10-27 | If \( \alpha \) and \( \beta \) are two different complex numbers with \( |\beta|=1 \), then \( ... |
2022-10-27 | The complex numbers \( \sin x+i \cos 2 x \) and \( \cos x-i \sin 2 x \), where \( i=\sqrt{-1} \)... |
2022-10-27 | If \( \frac{1-i x}{1+i x}=a-i b \) and \( a^{2}+b^{2}=1 \), where \( a, b \in R \) and \( i=\sqr... |
2022-10-27 | If \( z_{1}, z_{2} \) and \( z_{3}, z_{4} \) are two pairs of conjugate complex numbers, then \(... |
2022-10-27 | If \( \frac{3}{2+\cos \theta+i \sin \theta}=a+i b \), where \( i=\sqrt{-1} \) and \( a^{2}+b^{2}... |
2022-10-27 | The value of \( \sum_{n=0}^{50} i^{(2 n+1) !}( \) where, \( i=\sqrt{-1}) \) is
(a) \( i \)
(b) \... |
2022-10-27 | If \( \left|z_{1}-1\right| \leq 1,\left|z_{2}-2\right| \leq 2,\left|z_{3}-3\right| \leq 3 \), th... |
2022-10-27 | If \( \frac{z-1}{z+1} \) is purely imaginary, then \( |z| \) is equal to
(a) \( \frac{1}{2} \)
(... |
2022-10-27 | A line \( l \) passing through the origin is perpendicular to the lines
\( l_{1}:(3+t) \overline... |
2022-10-27 | The value of \( \sum_{r=-3}^{1003} i^{r}( \) where \( i=\sqrt{-1}) \) is
(a) 1
(b) \( -1 \)
(c) ... |
2022-10-27 | The least positive integer \( n \) for which \( \left(\frac{1+i}{1-i}\right)^{n}=\frac{2}{\pi}\l... |
2022-10-27 | If \( z=(3+4 i)^{6}+(3-4 i)^{6} \), where \( i=\sqrt{-1} \), then \( \operatorname{Im}(z) \) equ... |
2022-10-27 | The digit in the unit's place of \( (153)^{98} \) is (a) 1 (b) 3 (c) 7 |
2022-10-27 | If \( (x+i y)^{1 / 3}=a+i b \), where \( i=\sqrt{-1} \), then \( \left(\frac{x}{a}+\frac{y}{b}\r... |
2022-10-27 | If \( i=\sqrt{-1} \), the number of values of \( i^{n}+i^{-n} \) for different \( n \in I \) is
... |
2022-10-27 | Consider the following statements.
\( S_{1}:-6=2 i \times 3 i=\sqrt{(-4)} \times \sqrt{(-9)}( \)... |