If text{cis } alpha is the common value of (- | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $z_1 = (-1)^{1/4}$. We can write $-1 = \cos(\pi + 2k\pi) + i\sin(\pi + 2k\pi) = e^{i(\pi + 2k\pi)}$.Thus,$z_1 = e^{i(\frac{\pi}{4} + \frac{k\p

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(A) Let $z_1 = (-1)^{1/4}$. We can write $-1 = \cos(\pi + 2k\pi) + i\sin(\pi + 2k\pi) = e^{i(\pi + 2k\pi)}$.Thus,$z_1 = e^{i(\frac{\pi}{4} + \frac{k\pi}{2})}$ for $k = 0, 1, 2, 3$.The values are $e^{i\pi/4}, e^{i3\pi/4}, e^{i5\pi/4}, e^{i7\pi/4}$.Let $z_2 = (-i)^{1/2}$. We can write $-i = \cos(\frac{3\pi}{2} + 2n\pi) + i\sin(\frac{3\pi}{2} + 2n\pi) = e^{i(\frac{3\pi}{2} + 2n\pi)}$.Thus,$z_2 = e^{i(\frac{3\pi}{4} + n\pi)}$ for $n = 0, 1$.The values are $e^{i3\pi/4}$ and $e^{i7\pi/4}$.The common values are $e^{i3\pi/4}$ and $e^{i7\pi/4}$.For $e^{i3\pi/4}$,$\alpha = \frac{3\pi}{4}$,so $	an \alpha = 	an(\frac{3\pi}{4}) = -1$.For $e^{i7\pi/4}$,$\alpha = \frac{7\pi}{4}$,so $	an \alpha = 	an(\frac{7\pi}{4}) = -1$.Therefore,$	an \alpha = -1$.

If $\text{cis } \alpha$ is the common value of $(-1)^{1/4}$ and $(-i)^{1/2}$,then $\tan \alpha = $

Similar Questions

If $(\sqrt{3}-i)^{n}=2^{n}, n \in N$,then the least possible value of $n$ is

If $x = \sqrt{-1 - \sqrt{-1 - \sqrt{-1 - ... \infty}}}$, where $\omega$ is a non-real complex cube root of unity, then the value of $x$ is...

If $1, \alpha_1, \alpha_2, \alpha_3, \alpha_4$ are the roots of $z^5-1=0$ and $\omega$ is a cube root of unity,then $(\omega-1)(\omega-\alpha_1)(\omega-\alpha_2)(\omega-\alpha_3)(\omega-\alpha_4)+\omega$ is equal to

Let $\alpha$ and $\beta$ be the roots of $x^2 - \sqrt{2}x + 1 = 0$. Then the value of $\alpha^{50} + \beta^{50}$ is:

If $\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)$ where $x$ and $y$ are real, then the ordered pair $(x, y)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module