WBJEE · Maths · Complex Number
If \(\theta \in \mathbb{R}\) and \(\frac{1-i \cos \theta}{1+2 i \cos \theta}\) is real number, then \(\theta\) will be (when \(I:\) Set of integers)
- A \((2 n+1) \frac{\pi}{2}, n \in l\)
- B \(\frac{3 n \pi}{2}, n \in I\)
- C \(n \pi, n \in I\)
- D \(2 n \pi, n \in l\)
Answer & Solution
Correct Answer
(A) \((2 n+1) \frac{\pi}{2}, n \in l\)
Step-by-step Solution
Detailed explanation
Let \(Z=\frac{1-i \cos \theta}{1+2 i \cos \theta}\) \(\therefore \quad \bar{z}=\frac{1+i \cos \theta}{1-2 i \cos \theta}\) Since, \(z\) is a real number, then \(z-\bar{z}=0\) \(\Rightarrow \frac{1-i \cos \theta}{1+2 i \cos \theta}=\frac{1+i \cos \theta}{1-2 i \cos \theta}\)…
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 \(\alpha\) and \(\beta\) are the roots of \(x^{2}-p x+1=0\) and \(\gamma\) is a root of \(x^{2}+p x+1=0,\) then \((\alpha+\gamma)(\beta+\gamma)\) isWBJEE 2015 Medium
- \(\int \cos (\log x) d x=F(x)+C,\) where \(C\) is an arbitrary constant. Here, \(F(x)\) is equal toWBJEE 2017 Hard
- Three lines are drawn from the origin \(O\) with direction cosines proportional to (1,-1,1) (2,-3,0) and \((1,0,3) .\) The three lines areWBJEE 2017 Easy
- If \(\alpha, \beta\) be the roots of \(x^2-a(x-1)+b=0\), then the value of \(\frac{1}{\alpha^2-a \alpha}+\frac{1}{\beta^2-a \beta}+\frac{2}{a+b}\)WBJEE 2009 Easy
- Let \(f(\theta)=\left|\begin{array}{ccc}1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1\end{array}\right|\). Suppose \(A\) and \(B\) are respectively maximum and minimum values of \(f(\theta)\). Then \((A, B)\) is equal toWBJEE 2025 Medium
- Let \(R\) be the real line. Let the relations \(S\) and \(T\) on \(R\) be defined by \(S=\{(x, y): y=x+1,0 < x < 2\}, T=\{(x, y):(x-y)\) is an integer \(\}\). ThenWBJEE 2021 Medium
More PYQs from WBJEE
- The co-ordinates of the foot of the perpendicular from \((0,0)\) upon the line \(x+y=2\) areWBJEE 2009 Medium
- Identify the correct statements(s) :WBJEE 2024 Medium
- Molecular velocities of two gases at the same temperature \((\mathrm{T})\) are \(\mathrm{u}_{1}\) and \(\mathrm{u}_{2} .\) Their masses are \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\) respectively. Which of the following expressions is correct at temperature \(\mathrm{T} ?\)WBJEE 2021 Easy
- A circular disc rolls on a horizontal Iloor without slipping and the centre of the disc moves with a uniform velocity \(v\). Which of the following values of the velocily at a point on the rim of the disc can have?WBJEE 2015 Medium
- The system of linear equations \(\lambda x+y+z=3\)
\(x-y-2 z=6\)
\(-x+y+z=\mu\) hasWBJEE 2012 Easy - The plane \(\ell \mathrm{x}+\mathrm{my}=0\) is rotated about its line of intersection with the plane \(\mathrm{z}=0\) through an angle \(\alpha\). The equation changes toWBJEE 2021 Hard