If frac{3+2i sin theta}{1-2i sin theta} is a | vedclass

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

Question

(A) Let $z = \frac{3+2i \sin 	heta}{1-2i \sin 	heta}$.To make $z$ a real number,the imaginary part must be zero.Multiply the numerator and denominat

Vedclass · Accepted Answer

$\pi$

Vedclass · Answer

(A) Let $z = \frac{3+2i \sin 	heta}{1-2i \sin 	heta}$.To make $z$ a real number,the imaginary part must be zero.Multiply the numerator and denominator by the conjugate of the denominator $(1+2i \sin 	heta)$:$z = \frac{(3+2i \sin 	heta)(1+2i \sin 	heta)}{(1-2i \sin 	heta)(1+2i \sin 	heta)}$$z = \frac{3 + 6i \sin 	heta + 2i \sin 	heta + 4i^2 \sin^2 	heta}{1 + 4 \sin^2 	heta}$Since $i^2 = -1$,we have:$z = \frac{(3 - 4 \sin^2 	heta) + i(8 \sin 	heta)}{1 + 4 \sin^2 	heta}$For $z$ to be real,the imaginary part must be $0$:$\frac{8 \sin 	heta}{1 + 4 \sin^2 	heta} = 0$This implies $\sin 	heta = 0$.Given $0 < 	heta < 2\pi$,the only solution is $	heta = \pi$.

If $\frac{3+2i \sin \theta}{1-2i \sin \theta}$ is a real number and $0 < \theta < 2\pi$,then $\theta$ is equal to

Similar Questions

$\operatorname{sech}^{-1}(\sin \theta)$ is equal to

Which of the following is known as a fluid connective tissue?

$A$ short magnetic needle is pivoted in a uniform magnetic field of induction $1 ~T$. Now,simultaneously another magnetic field of induction $\sqrt{3} ~T$ is applied at right angles to the first field; the needle deflects through an angle $\theta$ whose value is (in $^{\circ}$)

Which of the following is not a synthetic polymer?

$A$ proton, a deuteron, and an $\alpha$-particle having the same momentum enter a region of uniform electric field between the parallel plates of a capacitor. The electric field is perpendicular to the initial path of the particles. Then the ratio of deflections suffered by them is

Vedclass Test Series

Exam Paper Generator

Online Exam Module