The values of x for which sin x + i cos 2x an | vedclass

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

Question

(B) Two complex numbers $z_1 = a + ib$ and $z_2 = c + id$ are conjugates if $a = c$ and $b = -d$. Given $z_1 = \sin x + i \cos 2x$ and $z_2 = \cos x -

Vedclass · Accepted Answer

None

Vedclass · Answer

(B) Two complex numbers $z_1 = a + ib$ and $z_2 = c + id$ are conjugates if $a = c$ and $b = -d$. Given $z_1 = \sin x + i \cos 2x$ and $z_2 = \cos x - i \sin 2x$. For these to be conjugates,we must have $\sin x = \cos x$ and $\cos 2x = -(-\sin 2x) = \sin 2x$. From $\sin x = \cos x$,we get $	an x = 1$,which implies $x = n\pi + \frac{\pi}{4}$. From $\cos 2x = \sin 2x$,we get $	an 2x = 1$,which implies $2x = m\pi + \frac{\pi}{4}$,or $x = \frac{m\pi}{2} + \frac{\pi}{8}$. Since there is no value of $x$ that satisfies both conditions simultaneously,there is no solution.

The values of $x$ for which $\sin x + i \cos 2x$ and $\cos x - i \sin 2x$ are conjugate to each other are

Similar Questions

If $f(x)$ is a polynomial of degree $n$ with rational coefficients and $1+2i, 2-\sqrt{3}$ and $5$ are three roots of $f(x)=0$,then the least value of $n$ is

If $z = x - iy$ and $z^{1/3} = p + iq$,then $\left( \frac{x}{p} + \frac{y}{q} \right) / (p^2 + q^2)$ is equal to

If one of the roots of the equation $4x^4 - 24x^3 + 57x^2 + 18x - 45 = 0$ is $3 + i\sqrt{6}$,find the other roots.

For a complex number $Z = a + ib$,let $\hat{Z} = b + ia$. If $Z_1$ and $Z_2$ are such complex numbers,then $\widehat{Z_1 Z_2} = $

The imaginary part of $\cosh(\alpha + i\beta)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module