JEE Mains · Maths · STD 11 - 4.1 complex nubers
All the points in the set \(S\, = \left\{ {\frac{{\alpha \, + \,i}}{{\alpha \, - \,i}}\,:\,\alpha \, \in \,R} \right\}\,(i\, = \,\sqrt { - 1} )\) lie on a
- A straight line whose slope is \(1\)
- B circle whose radius is \(\sqrt 2\)
- C straight line whose slope is \(- 1\)
- D circle whose radius is \(1\)
Answer & Solution
Correct Answer
(D) circle whose radius is \(1\)
Step-by-step Solution
Detailed explanation
Let \(\frac{{\alpha \, + \,i}}{{\alpha \, - \,i}}\, = z\) \( \Rightarrow \,\left| {\frac{{\alpha + i}}{{\alpha - i}}} \right|\, = \,\left| z \right|\) \( \Rightarrow \,1\, = \,\,\left| z \right|\) \( \Rightarrow \) circle of radius \(1\)
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
- \(\mathop \smallint \limits_2^4 \frac{{\log {x^2}}}{{\log {x^2} + {\rm{log}}\left( {36 - 12x + {x^2}} \right)}}\;dx = \)JEE Mains 2015 Medium
- If \(\mathrm{S}=\left\{\mathrm{z} \in \mathbb{C}: \frac{\mathrm{z}-i}{\mathrm{z}+2 i} \in \mathbb{R}\right\}\), then :JEE Mains 2021 Medium
- Let \(\theta_1\) be the angle between two lines \(2x + 3y + c_1\, = 0\) and \(-x+5y + c_2\, = 0\) and \(\theta_2\) be the angle between two lines \(2x+ 3y + c_1\, = 0\) and \(-x+ 5y + c_3\, = 0\), where \(c_1, c_2, c_3\) are any real numbers Statement \(-1\) : If \(c_2\) and \(c_3\) are proportional, then \(\theta_1\, = \theta_2\) Statement \(-2\) : \(\theta_1\, = \theta_2\) for all \(c_2\) and \(c_3\)JEE Mains 2013 Hard
- The range of \(a \in R\) for which the function \( f(x)=(4 a-3)\left(x+\log _{e} 5\right)+2(a-7) \cot \left(\frac{x}{2}\right) \sin ^{2}\left(\frac{x}{2}\right)\) \(x \neq 2 n \pi, n \in N ,\) has critical points, isJEE Mains 2021 Hard
- Let the mean and the variance of seven observations \(2, 4, \alpha, 8, \beta, 12, 14\), \(\alpha < \beta\), be \(8\) and \(16\) respectively. Then the quadratic equation whose roots are \(3\alpha + 2\) and \(2\beta + 1\) is :JEE Mains 2026 Medium
- If \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{ll}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}\), and \(\mathrm{Q}=\mathrm{A}^{\mathrm{T}} \mathrm{BA}\), then the inverse of the matrix \(\mathrm{A} \mathrm{Q}^{2021} \mathrm{~A}^{\mathrm{T}}\) is equal to :JEE Mains 2021 Hard
More PYQs from JEE Mains
- \(\lim _{n \rightarrow \infty} \frac{1}{2^{n}}\left(\frac{1}{\sqrt{1-\frac{1}{2^{a}}}}+\frac{1}{\sqrt{1-\frac{2}{2^{n}}}}+\frac{1}{\sqrt{1-\frac{3}{2^{a}}}}+\ldots \ldots+\frac{1}{\sqrt{1-\frac{2^{a}-1}{2^{n}}}}\right)\) is equal toJEE Mains 2022 Hard
- Consider the function \(f:(0, \infty) \rightarrow R\) defined by \(f(x)=e^{-\left|\log _e x\right|}\). If \(m\) and \(n\) be respectively the number of points at which \(f\) is not continuous and \(f\) is not differentiable, then \(\mathrm{m}+\mathrm{n}\) isJEE Mains 2024 Hard
- The integral \(\int \limits_{0}^{2} \| x-1|-x| d x\) is equal toJEE Mains 2020 Hard
- Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a polynomial function of degree four having extreme values at \(x=4\) and \(x=5\).
If \(\lim _{x \rightarrow 0} \frac{f(x)}{x^2}=5\), then \(f(2)\) is equal to :JEE Mains 2025 Medium - Given; A circle \(2{x^2} + 2{y^2} = 5\) and parabola \({y^2} = 4\sqrt 5 x\) Statement \(-1\):An equation of a common tangent to these curve is \(y = x + \sqrt 5 \) Statement \(-2\): If the line, \(y = mx + \frac{{\sqrt 5 }}{m}\left( {m \ne 0} \right)\) is their common tangent , then \(m\) satisfies \({m^4} - 3{m^2} + 2 = 0\).JEE Mains 2013 Hard
- Locus of the image of point \( (2,3)\) in the line \(\left( {2x - 3y + 4} \right) + k\left( {x - 2y + 3} \right) = 0,k \in R\) is a:JEE Mains 2015 Hard