AP EAMCET · Maths · Complex Number
If \(\frac{3-2 i \sin \theta}{1+2 i \sin \theta}\) is purely imaginary number, then \(\theta=\)
- A \(2 n \pi \pm \frac{\pi}{4}\)
- B \(2 n \pi \pm \frac{\pi}{2}\)
- C \(n \pi \pm \frac{\pi}{3}\)
- D \(n \pi \pm \frac{\pi}{6}\)
Answer & Solution
Correct Answer
(C) \(n \pi \pm \frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(\frac{3-2 i \sin \theta}{1+2 i \sin \theta}=\frac{(3-2 i \sin \theta)(1-2 i \sin \theta)}{1+4 \sin ^2 \theta}=\frac{3-4 \sin ^2 \theta}{1+4 \sin ^2 \theta}\) From the given information real part \(=0\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If a system of circles pass through \((2,3)\) and cuts the circle \(x^2+y^2=12\) orthogonally, then the equation of the locus of the centres of that system of circles, isAP EAMCET 2018 Medium
- If the system of linear equations given by is consistent and if is a solution, thenAP EAMCET 2018 Easy
- If a point moves along the ellipse and if is the centre of the ellipse, then the sum of maximum and minimum values of isAP EAMCET 2021 Medium
- All the letters of the word ANIMAL are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. If the rank of the word ANIMAL is \(x\), then the permutation with rank \(x\), among the permutations obtained by permuting the letters of the word PERSON and arranging the permutations thus formed in dictionary order isAP EAMCET 2019 Medium
- The number of solutions of the equation \(2 \sin ^2 \theta-3 \cos ^2 \theta=\sin \theta \cos \theta\) lying in the interval \((-\pi, \pi)\) isAP EAMCET 2025 Medium
- If \(f(2)=4\) and \(f^{\prime}(2)=1\), then
\[
\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}
\]
is equal toAP EAMCET 2008 Medium
More PYQs from AP EAMCET
- In compound \((\mathrm{X})\), hyperconjugation is present and in \((\mathrm{Y})\), resonance effect is present. What are X and Y, respectively?AP EAMCET 2025 Medium
- Find the length of the intercept cut by the pair of lines \(2 x^2+4 x y-4 y^2-6 x-8 y+7=0\) over the \(Y\)-axisAP EAMCET 2021 Easy
- Three Carnot engines operate in series between a heat source at temperature \(T_1\) and heat sink at a temperature \(T_4\). There are two other reservoirs at temperatures \(T_2\) and \(T_3\). The three engines are equally efficient, if (given that, \(\left.T_1>T_2>T_3>T_4\right)\)
AP EAMCET 2021 Hard - A circular portion of radius \(R_2\) has been removed from one edge of a circular disc of radius \(R_1\). The correct expression for the centre of mass for the remaining portion of the disc isAP EAMCET 2022 Easy
- The general solution of the differential equation \(x d y-y d x=\sqrt{x^2+y^2} d x\) isAP EAMCET 2024 Medium
- The area of the triangle formed by the tangent to the curve \(x y=\mathrm{a}^2\) at \(\left(x_1, y_1\right)\) on it and the axes isAP EAMCET 2022 Medium