TS EAMCET · Maths · Complex Number
The locus of \(z\) satisfying the inequality \(\left|\frac{z+2 i}{2 z+i}\right| < 1\), where \(z=x+i y\), is
- A \(x^2+y^2 < 1\)
- B \(x^2-y^2 < 1\)
- C \(x^2+y^2>1\)
- D \(2 x^2+3 y^2 < 1\)
Answer & Solution
Correct Answer
(C) \(x^2+y^2>1\)
Step-by-step Solution
Detailed explanation
Let \(z=x+i y\) Given, \(\quad\left|\frac{z+2 i}{2 z+i}\right| 3 \\ \Rightarrow & x^2+y^2>1\end{array}\)
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
- The origin belongs to a region between the lines \(x+2 y-5=0\) and \(3 x-4 y+5=0\). The number of points in that region of the form \(\left((\alpha-1)^2, \alpha\right), \alpha \in Z\) isTS EAMCET 2021 Medium
- If \(\mathrm{p}_1, \mathrm{p}_2, \mathrm{p}_3\) are the altitudes and \(a=4, b=5, c=6\) are the sides of a triangle ABC, then \(\frac{1}{\mathrm{p}_1{ }^2}+\frac{1}{\mathrm{p}_2{ }^2}+\frac{1}{\mathrm{p}_3{ }^2}=\)TS EAMCET 2025 Medium
- \(\alpha, \beta, \gamma\) are the roots of the equation \(8 x^3-42 x^2+63 x-27=0\) If \(\beta \lt \gamma \lt \alpha\) and \(\beta, \gamma, \alpha\) are in geometric progression, then the extreme value of the expression \(\gamma x^2+4 \beta x+\alpha\) isTS EAMCET 2024 Medium
- If \(2 x^2-3 x y+4 y^2+2 x-3 y+4=0\), then \(\left(\frac{d y}{d x}\right)_{(3,2)}=\)TS EAMCET 2024 Easy
- If \(\frac{(1+i) x-i}{2+i}+\frac{(1+2 i) y+i}{2-i}=1\), then \((x, y)\) is equal toTS EAMCET 2013 Easy
- The cosine of the angle \(A\) of the triangle with vertices \(A(1,-1,2), B(6,11,2), C(1,2,6)\) isTS EAMCET 2007 Easy
More PYQs from TS EAMCET
- In a triangle ABC, if \(c^2-a^2=b(\sqrt{3} c-b)\) and \(b^2-a^2=c(c-a)\), then \(\lfloor\mathrm{ACB}=\)TS EAMCET 2025 Hard
- The product of lengths of the perpendiculars from any point of the hyperbola \(x^2-y^2=8\) to its asymptotes isTS EAMCET 2019 Medium
- A ball is dropped from a height \(h\) on a floor of coefficient of restitution \(e\). The total distance covered by the ball just before second hit isTS EAMCET 2008 Medium
- If \(f:[2,3] \rightarrow R\) is defined by \(f(x)=x^3+3 x-2\), then the range \(f(x)\) is contained in the intervalTS EAMCET 2009 Easy
- Match the following:
The correct answer isTS EAMCET 2024 Easy - Which of the following does not follow first law of thermodynamics? work heat change in internal energyTS EAMCET 2019 Easy