AP EAMCET · Maths · Complex Number
The locus of the point \(z=x+i y\) satisfying the equation \(\left|\frac{z-1}{z+1}\right|=1\) is given by :
- A \(x=0\)
- B \(y=0\)
- C \(x=y\)
- D \(x+y=0\)
Answer & Solution
Correct Answer
(A) \(x=0\)
Step-by-step Solution
Detailed explanation
\(\because \quad\left|\frac{z-1}{z+1}\right|=1\) \(\Rightarrow \quad\left|\frac{x+i y-1}{x+i y+1}\right|=1\) \(\Rightarrow \quad|(x-1)+i y|=|(x+1)+i y|\) \(\Rightarrow \quad \sqrt{(x-1)^2+y^2}=\sqrt{(x+1)^2+y^2}\) \(\Rightarrow \quad x^2-2 x+1+y^2=x^2+1+2 x+y^2\)…
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 \(f(2)=4\) 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 - The circle \(x^2+y^2-8 x-12 y+\alpha=0\) lies in the first quadrant without touching the coordinate axes. If \((6,6)\) is an interior point to the circle, thenAP EAMCET 2024 Easy
- If \(m_1, m_2, m_3\) and \(m_4\) are respectively the magnitudes of the vectors
\(\overrightarrow{\mathbf{a}}_1=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \quad \overrightarrow{\mathbf{a}}_2=3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}\),
\(\overrightarrow{\mathbf{a}}_3=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}} \quad\) and \(\quad \overrightarrow{\mathbf{a}}_4=-\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\),
then the correct order of \(m_1, m_2, m_3\) and \(m_4\) isAP EAMCET 2009 Easy - A straight line \(L\) cuts both the lines \(5 x-y-4=0\) and \(3 x+4 y-4=0\). The segment of \(L\) between the two lines is bisected at the point \((1,5)\). The equation of \(L\) isAP EAMCET 2017 Medium
- If the orthocenter and circumcenter of a triangle respectively are \((3,-4,2)\) and \((2,1,3)\), then its centroid isAP EAMCET 2021 Medium
- If \(f(t)=\frac{1+\operatorname{cosec} t}{1-\operatorname{cosec} t}\) for \(0 < t < \frac{\pi}{2}\) and \(f^{\prime}(t)=f(t) g(t)\), then \(g(t)=\)AP EAMCET 2019 Easy
More PYQs from AP EAMCET
- Two particles of masses \(1 \mathrm{~g}\) and \(2 \mathrm{~g}\) move towards each other with velocities \(10 \mathrm{~ms}^{-1}\) and \(20 \mathrm{~ms}^{-1}\) respectively. The velocity of the centre of mass of the system of the two particles isAP EAMCET 2023 Easy
- The cartesian equation of the plane whose vector equation is \(\gamma=(1+\lambda-\mu) \hat{\mathbf{i}}+(2-\lambda) \hat{\mathbf{j}}+(3-2 \lambda+2 \mu) \hat{\mathbf{k}}\) where \(\lambda, \mu\) are scalars, isAP EAMCET 2016 Easy
- \(\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}+\operatorname{cosec} 384^{\circ}=\)AP EAMCET 2025 Medium
- In which of the following, the sol is not correctly matched with respect to its charge?
I. \(\mathrm{Al}_2 \mathrm{O}_3 \cdot \mathrm{x} \cdot \mathrm{H}_2 \mathrm{O}\) sol; + ve sol
II. Starch sol; +ve sol
III. \(\mathrm{TiO}_2\) sol; -ve sol
IV. Methylene blue sol; +ve sol
The correct answer isAP EAMCET 2023 Easy - Identify the incorrect statement regarding Reynold's numberAP EAMCET 2021 Easy
- Let \(N\) be the set of all natural numbers, \(Z\) be the set of all integers and \(\sigma: N \rightarrow Z\) be defined by
\[
\sigma(n)=\left\{\begin{array}{ccc}
\frac{n}{2}, & \text { if } & n \text { is even } \\
-\frac{n-1}{2}, & \text { if } & n \text { is odd }
\end{array}\right. \text {. Then, }
\]AP EAMCET 2017 Easy