TS EAMCET · Maths · Complex Number
If \(z\) is a complex number such that \(|z+4| \geq 3\), then the smallest value of \(|z+3|\) is
- A 3
- B 1
- C 2
- D 0
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { }|z+4| \geq 3 \\ & |z+3+1| \leq|z+3|+1 \\ & |z+3|+1 \geq 3 \Rightarrow|z+3| \geq 2 \end{aligned} \] \(\therefore\) Smallest value of \(|z+3|=2\)
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 \(\frac{2 \sin \theta}{1+\cos \theta+\sin \theta}=y\), then \(\frac{1-\cos \theta+\sin \theta}{1+\sin \theta}=\)TS EAMCET 2023 Easy
- \(7 x+y-24=0\) and \(x+7 y-24=0\) represent the equal sides of an isosceles triangle. If the third side passes through \((-1,1)\) then a possible equation for the third side isTS EAMCET 2024 Medium
- If \(\cosh \beta=\sec \alpha \cos \theta, \sinh \beta=\operatorname{cosec} \alpha \sin \theta\), then \(\sinh ^2 \beta=\)TS EAMCET 2018 Easy
- The volume of the tetrahedron with \(\hat{i}-\lambda \hat{j}+\hat{k}, \lambda \hat{i}-\hat{j}-\hat{k}\) and \(\hat{i}+\hat{j}+\lambda \hat{k}\) as coterminous edges is 2 . If \(\lambda\) is an integer, then \(|\lambda \hat{\mathrm{i}}-3 \lambda \hat{\mathrm{j}}+3 \hat{\mathrm{k}}|=\)TS EAMCET 2023 Medium
- A cube having edge of length is painted on all faces and then it is cut into equal cubes of unit volume. A small cube is selected at random and found that a face of it is painted, then the probability that two more faces of it are also painted isTS EAMCET 2022 Medium
- \(y=\log \left\{\left(\frac{1+x}{1-x}\right)^{1 / 4}\right\}-\frac{1}{2} \tan ^{-1}(x)\), then \(\frac{d y}{d x}\) is equal toTS EAMCET 2007 Hard
More PYQs from TS EAMCET
- 1. The focal lengths of the objective and the eyepiece of a compound microscope are \(2 \mathrm{~cm}\) and \(3 \mathrm{~cm}\) respectively and the distance between them is \(15 \mathrm{~cm}\). The final image formed by the eyepiece is at infinity. The distances of the object and the image produced by the object from the objective lens are respectivelyTS EAMCET 2023 Easy
- If and the angle between and is then the area of the triangle (in square units) with and as two of its sides isTS EAMCET 2021 Easy
- The locus of a point such that the sum of its distances from the points \((0,2)\) and \((0,-2)\) is 6 , isTS EAMCET 2011 Medium
- Which of the following is the unit of mobility of a electron in a conductor?TS EAMCET 2022 Easy
- If \(A+B+C=\frac{\pi}{4}\), then \(4 \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}-\cos \frac{\pi}{8}=\)TS EAMCET 2018 Medium
- Two long straight parallel wires carry currents of 8 A and 10 A in opposite directions. If the distance of separation between the wires is 9 cm, then the net magnetic field at a point between the two wires, which is at a perpendicular distance of 4 cm from the wire carrying 8 A current isTS EAMCET 2025 Medium